Linear Algebra Examples

$- 3 (5 - 6 x) = 6 - (4 x - (7 x - (6 x - (3 x + 33))))$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$6 - (4 x - (7 x - (6 x - (3 x + 33)))) = - 3 (5 - 6 x)$

Step 2

Simplify $6 - (4 x - (7 x - (6 x - (3 x + 33))))$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Simplify each term.

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Step 2.1.1.1.1.1

Apply the distributive property.

$6 - (4 x - (7 x - (6 x - (3 x) - 1 \cdot 33))) = - 3 (5 - 6 x)$

Step 2.1.1.1.1.2

Multiply $3$ by $- 1$ .

$6 - (4 x - (7 x - (6 x - 3 x - 1 \cdot 33))) = - 3 (5 - 6 x)$

Step 2.1.1.1.1.3

Multiply $- 1$ by $33$ .

$6 - (4 x - (7 x - (6 x - 3 x - 33))) = - 3 (5 - 6 x)$

Step 2.1.1.1.2

Subtract $3 x$ from $6 x$ .

$6 - (4 x - (7 x - (3 x - 33))) = - 3 (5 - 6 x)$

Step 2.1.1.1.3

Apply the distributive property.

$6 - (4 x - (7 x - (3 x) - - 33)) = - 3 (5 - 6 x)$

Step 2.1.1.1.4

Multiply $3$ by $- 1$ .

$6 - (4 x - (7 x - 3 x - - 33)) = - 3 (5 - 6 x)$

Step 2.1.1.1.5

Multiply $- 1$ by $- 33$ .

$6 - (4 x - (7 x - 3 x + 33)) = - 3 (5 - 6 x)$

Step 2.1.1.2

Subtract $3 x$ from $7 x$ .

$6 - (4 x - (4 x + 33)) = - 3 (5 - 6 x)$

Step 2.1.1.3

Apply the distributive property.

$6 - (4 x - (4 x) - 1 \cdot 33) = - 3 (5 - 6 x)$

Step 2.1.1.4

Multiply $4$ by $- 1$ .

$6 - (4 x - 4 x - 1 \cdot 33) = - 3 (5 - 6 x)$

Step 2.1.1.5

Multiply $- 1$ by $33$ .

$6 - (4 x - 4 x - 33) = - 3 (5 - 6 x)$

Step 2.1.2

Subtract $4 x$ from $4 x$ .

$6 - (0 - 33) = - 3 (5 - 6 x)$

Step 2.1.3

Subtract $33$ from $0$ .

$6 - - 33 = - 3 (5 - 6 x)$

Step 2.1.4

Multiply $- 1$ by $- 33$ .

$6 + 33 = - 3 (5 - 6 x)$

Step 2.2

Add $6$ and $33$ .

$39 = - 3 (5 - 6 x)$

Step 3

Simplify $- 3 (5 - 6 x)$ .

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Step 3.1

Apply the distributive property.

$39 = - 3 \cdot 5 - 3 (- 6 x)$

Step 3.2

Multiply.

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Step 3.2.1

Multiply $- 3$ by $5$ .

$39 = - 15 - 3 (- 6 x)$

Step 3.2.2

Multiply $- 6$ by $- 3$ .

$39 = - 15 + 18 x$

Step 4

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$- 15 + 18 x = 39$

Step 5

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

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Step 5.1

Add $15$ to both sides of the equation.

$18 x = 39 + 15$

Step 5.2

Add $39$ and $15$ .

$18 x = 54$

Step 6

Divide each term in $18 x = 54$ by $18$ and simplify.

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Step 6.1

Divide each term in $18 x = 54$ by $18$ .

$\frac{18 x}{18} = \frac{54}{18}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $18$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{18 x}{18} = \frac{54}{18}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x = \frac{54}{18}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $54$ by $18$ .

$x = 3$

Step 7

The domain is the set of all valid $x$ values.

${x | x = 3}$

Step 8