Finite Math Examples

$3 x - 2 y + 4 z = 9$ , $- 6 x + 4 y - 8 z = k$

Step 1

Solve the equation for $y$ .

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Move all terms not containing $y$ to the right side of the equation.

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Subtract $3 x$ from both sides of the equation.

$- 2 y + 4 z = 9 - 3 x$

$- 6 x + 4 y - 8 z = k$

Subtract $4 z$ from both sides of the equation.

$- 2 y = 9 - 3 x - 4 z$

$- 6 x + 4 y - 8 z = k$

$- 2 y = 9 - 3 x - 4 z$

$- 6 x + 4 y - 8 z = k$

Divide each term in $- 2 y = 9 - 3 x - 4 z$ by $- 2$ and simplify.

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Divide each term in $- 2 y = 9 - 3 x - 4 z$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{9}{- 2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

Simplify the left side.

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Cancel the common factor of $- 2$ .

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Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{9}{- 2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

Divide $y$ by $1$ .

$y = \frac{9}{- 2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

$y = \frac{9}{- 2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

$y = \frac{9}{- 2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

Simplify the right side.

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Simplify each term.

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Move the negative in front of the fraction.

$y = - \frac{9}{2} + \frac{- 3 x}{- 2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

Dividing two negative values results in a positive value.

$y = - \frac{9}{2} + \frac{(3) x}{2} + \frac{- 4 z}{- 2}$

$- 6 x + 4 y - 8 z = k$

Cancel the common factor of $- 4$ and $- 2$ .

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Factor $- 2$ out of $- 4 z$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + \frac{- 2 (2 z)}{- 2}$

$- 6 x + 4 y - 8 z = k$

Cancel the common factors.

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Factor $- 2$ out of $- 2$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + \frac{- 2 (2 z)}{- 2 \cdot 1}$

$- 6 x + 4 y - 8 z = k$

Cancel the common factor.

$y = - \frac{9}{2} + \frac{3 x}{2} + \frac{- 2 (2 z)}{- 2 \cdot 1}$

$- 6 x + 4 y - 8 z = k$

Rewrite the expression.

$y = - \frac{9}{2} + \frac{3 x}{2} + \frac{2 z}{1}$

$- 6 x + 4 y - 8 z = k$

Divide $2 z$ by $1$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 4 y - 8 z = k$

Step 2

Solve the equation for $z$ .

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Simplify $- 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 z) - 8 z$ .

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Simplify each term.

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Apply the distributive property.

$- 6 x + 4 (- \frac{9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Simplify.

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Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{9}{2}$ into the numerator.

$- 6 x + 4 (\frac{- 9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Factor $2$ out of $4$ .

$- 6 x + 2 (2) (\frac{- 9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor.

$- 6 x + 2 \cdot (2 (\frac{- 9}{2})) + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite the expression.

$- 6 x + 2 \cdot - 9 + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x + 2 \cdot - 9 + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $2$ by $- 9$ .

$- 6 x - 18 + 4 (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$- 6 x - 18 + 2 (2) (\frac{3 x}{2}) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor.

$- 6 x - 18 + 2 \cdot (2 (\frac{3 x}{2})) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite the expression.

$- 6 x - 18 + 2 (3 x) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x - 18 + 2 (3 x) + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $3$ by $2$ .

$- 6 x - 18 + 6 x + 4 (2 z) - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $2$ by $4$ .

$- 6 x - 18 + 6 x + 8 z - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x - 18 + 6 x + 8 z - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 6 x - 18 + 6 x + 8 z - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Combine the opposite terms in $- 6 x - 18 + 6 x + 8 z - 8 z$ .

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Add $- 6 x$ and $6 x$ .

$0 - 18 + 8 z - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Subtract $18$ from $0$ .

$- 18 + 8 z - 8 z = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Subtract $8 z$ from $8 z$ .

$- 18 + 0 = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $- 18$ and $0$ .

$- 18 = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 18 = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$- 18 = k$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite $- 18 = k$ so $k$ is on the left side.

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

The variable $z$ got canceled.

All real numbers

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

All real numbers

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Step 3

Solve the equation for $k$ .

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Rewrite the equation as $k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l \cdot l (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l \cdot l (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Simplify $- 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l \cdot l (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$ .

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Simplify each term.

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Simplify each term.

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Multiply $l$ by $l$ by adding the exponents.

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Move $l$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l) (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l$ by $l$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{2} (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{2} (r e a l) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l^{2}$ by $l$ by adding the exponents.

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Move $l$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l^{2}) (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l$ by $l^{2}$ .

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Raise $l$ to the power of $1$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l^{2}) (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{1 + 2} (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{1 + 2} (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $1$ and $2$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r e a) (n u m b e r s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $r$ by $r$ by adding the exponents.

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Move $r$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r \cdot r e a) (n u m b e s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $r$ by $r$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r^{2} e a) (n u m b e s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r^{2} e a) (n u m b e s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite using the commutative property of multiplication.

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (e A l^{3} r^{2} a (n u m b e s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $e A l^{3} r^{2} a (n u m b e s)$ .

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Raise $e$ to the power of $1$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b (e e) s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Raise $e$ to the power of $1$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b (e e) s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{1 + 1} s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $1$ and $1$ .

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{2} s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{2} s))) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite using the commutative property of multiplication.

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 4 (- \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Apply the distributive property.

$k = - 6 x + 4 (- \frac{9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Simplify.

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Cancel the common factor of $2$ .

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Move the leading negative in $- \frac{9}{2}$ into the numerator.

$k = - 6 x + 4 (\frac{- 9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Factor $2$ out of $4$ .

$k = - 6 x + 2 (2) (\frac{- 9}{2}) + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor.

$k = - 6 x + 2 \cdot (2 (\frac{- 9}{2})) + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite the expression.

$k = - 6 x + 2 \cdot - 9 + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x + 2 \cdot - 9 + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $2$ by $- 9$ .

$k = - 6 x - 18 + 4 (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

$k = - 6 x - 18 + 2 (2) (\frac{3 x}{2}) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Cancel the common factor.

$k = - 6 x - 18 + 2 \cdot (2 (\frac{3 x}{2})) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite the expression.

$k = - 6 x - 18 + 2 (3 x) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 2 (3 x) + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $3$ by $2$ .

$k = - 6 x - 18 + 6 x + 4 (2 e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $2$ by $4$ .

$k = - 6 x - 18 + 6 x + 8 (e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 (e^{2} A l^{3} r^{2} a n u m b s) - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Remove parentheses.

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l \cdot l (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l$ by $l$ by adding the exponents.

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Move $l$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A (l \cdot l) (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l$ by $l$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{2} (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{2} (r e a l) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l^{2}$ by $l$ by adding the exponents.

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Move $l$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A (l \cdot l^{2}) (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $l$ by $l^{2}$ .

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Raise $l$ to the power of $1$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A (l \cdot l^{2}) (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{1 + 2} (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{1 + 2} (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $1$ and $2$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} (r e a) (n u m b e r s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $r$ by $r$ by adding the exponents.

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Move $r$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} (r \cdot r e a) (n u m b e s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $r$ by $r$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} (r^{2} e a) (n u m b e s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} (r^{2} e a) (n u m b e s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite using the commutative property of multiplication.

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (e A l^{3} r^{2} a (n u m b e s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Multiply $e A l^{3} r^{2} a (n u m b e s)$ .

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Raise $e$ to the power of $1$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} r^{2} a (n u m b (e e) s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Raise $e$ to the power of $1$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} r^{2} a (n u m b (e e) s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} r^{2} a (n u m b e^{1 + 1} s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $1$ and $1$ .

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} r^{2} a (n u m b e^{2} s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 (A l^{3} r^{2} a (n u m b e^{2} s))$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Rewrite using the commutative property of multiplication.

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 e^{2} A l^{3} r^{2} a n u m b s$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 e^{2} A l^{3} r^{2} a n u m b s$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Combine the opposite terms in $- 6 x - 18 + 6 x + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 e^{2} A l^{3} r^{2} a n u m b s$ .

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Add $- 6 x$ and $6 x$ .

$k = 0 - 18 + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 e^{2} A l^{3} r^{2} a n u m b s$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Subtract $18$ from $0$ .

$k = - 18 + 8 e^{2} A l^{3} r^{2} a n u m b s - 8 e^{2} A l^{3} r^{2} a n u m b s$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Subtract $8 e^{2} A l^{3} r^{2} a n u m b s$ from $8 e^{2} A l^{3} r^{2} a n u m b s$ .

$k = - 18 + 0$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Add $- 18$ and $0$ .

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 z$

Step 4

Simplify the right side.

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Simplify each term.

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Multiply $l$ by $l$ by adding the exponents.

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Move $l$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l) (r e a l) (n u m b e r s))$

$k = - 18$

Multiply $l$ by $l$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{2} (r e a l) (n u m b e r s))$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{2} (r e a l) (n u m b e r s))$

$k = - 18$

Multiply $l^{2}$ by $l$ by adding the exponents.

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Move $l$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l^{2}) (r e a) (n u m b e r s))$

$k = - 18$

Multiply $l$ by $l^{2}$ .

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Raise $l$ to the power of $1$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A (l \cdot l^{2}) (r e a) (n u m b e r s))$

$k = - 18$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{1 + 2} (r e a) (n u m b e r s))$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{1 + 2} (r e a) (n u m b e r s))$

$k = - 18$

Add $1$ and $2$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r e a) (n u m b e r s))$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r e a) (n u m b e r s))$

$k = - 18$

Multiply $r$ by $r$ by adding the exponents.

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Move $r$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r \cdot r e a) (n u m b e s))$

$k = - 18$

Multiply $r$ by $r$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r^{2} e a) (n u m b e s))$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} (r^{2} e a) (n u m b e s))$

$k = - 18$

Rewrite using the commutative property of multiplication.

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (e A l^{3} r^{2} a (n u m b e s))$

$k = - 18$

Multiply $e A l^{3} r^{2} a (n u m b e s)$ .

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Raise $e$ to the power of $1$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b (e e) s))$

$k = - 18$

Raise $e$ to the power of $1$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b (e e) s))$

$k = - 18$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{1 + 1} s))$

$k = - 18$

Add $1$ and $1$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{2} s))$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 (A l^{3} r^{2} a (n u m b e^{2} s))$

$k = - 18$

Rewrite using the commutative property of multiplication.

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s$

$k = - 18$

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s$

$k = - 18$

Step 5

Simplify the right side.

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Simplify $- \frac{9}{2} + \frac{3 x}{2} + 2 e^{2} A l^{3} r^{2} a n u m b s$ .

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Move $e^{2}$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 A l^{3} r^{2} a n u m b s e^{2}$

$k = - 18$

Move $A$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 l^{3} r^{2} a n u m b s A e^{2}$

$k = - 18$

Move $u$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 l^{3} r^{2} a n m b s u A e^{2}$

$k = - 18$

Move $r^{2}$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 l^{3} a n m b r^{2} s u A e^{2}$

$k = - 18$

Move $n$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 l^{3} a m b n r^{2} s u A e^{2}$

$k = - 18$

Move $m$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 l^{3} a b m n r^{2} s u A e^{2}$

$k = - 18$

Move $l^{3}$ .

$y = - \frac{9}{2} + \frac{3 x}{2} + 2 a b l^{3} m n r^{2} s u A e^{2}$

$k = - 18$

Move $- \frac{9}{2}$ .

$y = \frac{3 x}{2} + 2 a b l^{3} m n r^{2} s u A e^{2} - \frac{9}{2}$

$k = - 18$

Reorder $\frac{3 x}{2}$ and $2 a b l^{3} m n r^{2} s u A e^{2}$ .

$y = 2 a b l^{3} m n r^{2} s u A e^{2} + \frac{3 x}{2} - \frac{9}{2}$

$k = - 18$

$y = 2 a b l^{3} m n r^{2} s u A e^{2} + \frac{3 x}{2} - \frac{9}{2}$

$k = - 18$

$y = 2 a b l^{3} m n r^{2} s u A e^{2} + \frac{3 x}{2} - \frac{9}{2}$

$k = - 18$