Finite Math Examples

$5 - \frac{2}{3 h} = 2 a + a x - 1$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$- \frac{2}{3 h} = 2 a + a x - 1 - 5$

Step 1.2

Subtract $5$ from $- 1$ .

$- \frac{2}{3 h} = 2 a + a x - 6$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$3 h, 1, 1, 1$

Step 2.2

The LCM of one and any expression is the expression.

$3 h$

Step 3

Multiply each term in $- \frac{2}{3 h} = 2 a + a x - 6$ by $3 h$ to eliminate the fractions.

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Step 3.1

Multiply each term in $- \frac{2}{3 h} = 2 a + a x - 6$ by $3 h$ .

$- \frac{2}{3 h} (3 h) = 2 a (3 h) + a x (3 h) - 6 (3 h)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3 h$ .

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Step 3.2.1.1

Move the leading negative in $- \frac{2}{3 h}$ into the numerator.

$\frac{- 2}{3 h} (3 h) = 2 a (3 h) + a x (3 h) - 6 (3 h)$

Step 3.2.1.2

Cancel the common factor.

$\frac{- 2}{3 h} (3 h) = 2 a (3 h) + a x (3 h) - 6 (3 h)$

Step 3.2.1.3

Rewrite the expression.

$- 2 = 2 a (3 h) + a x (3 h) - 6 (3 h)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite using the commutative property of multiplication.

$- 2 = 2 \cdot 3 a h + a x (3 h) - 6 (3 h)$

Step 3.3.1.2

Multiply $2$ by $3$ .

$- 2 = 6 a h + a x (3 h) - 6 (3 h)$

Step 3.3.1.3

Rewrite using the commutative property of multiplication.

$- 2 = 6 a h + 3 a x h - 6 (3 h)$

Step 3.3.1.4

Multiply $3$ by $- 6$ .

$- 2 = 6 a h + 3 a x h - 18 h$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $6 a h + 3 a x h - 18 h = - 2$ .

$6 a h + 3 a x h - 18 h = - 2$

Step 4.2

Factor $3 h$ out of $6 a h + 3 a x h - 18 h$ .

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Step 4.2.1

Factor $3 h$ out of $6 a h$ .

$3 h (2 a) + 3 a x h - 18 h = - 2$

Step 4.2.2

Factor $3 h$ out of $3 a x h$ .

$3 h (2 a) + 3 h (a x) - 18 h = - 2$

Step 4.2.3

Factor $3 h$ out of $- 18 h$ .

$3 h (2 a) + 3 h (a x) + 3 h (- 6) = - 2$

Step 4.2.4

Factor $3 h$ out of $3 h (2 a) + 3 h (a x)$ .

$3 h (2 a + a x) + 3 h (- 6) = - 2$

Step 4.2.5

Factor $3 h$ out of $3 h (2 a + a x) + 3 h (- 6)$ .

$3 h (2 a + a x - 6) = - 2$

Step 4.3

Divide each term in $3 h (2 a + a x - 6) = - 2$ by $3 (2 a + a x - 6)$ and simplify.

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Step 4.3.1

Divide each term in $3 h (2 a + a x - 6) = - 2$ by $3 (2 a + a x - 6)$ .

$\frac{3 h (2 a + a x - 6)}{3 (2 a + a x - 6)} = \frac{- 2}{3 (2 a + a x - 6)}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 h (2 a + a x - 6)}{3 (2 a + a x - 6)} = \frac{- 2}{3 (2 a + a x - 6)}$

Step 4.3.2.1.2

Rewrite the expression.

$\frac{h (2 a + a x - 6)}{2 a + a x - 6} = \frac{- 2}{3 (2 a + a x - 6)}$

Step 4.3.2.2

Cancel the common factor of $2 a + a x - 6$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{h (2 a + a x - 6)}{2 a + a x - 6} = \frac{- 2}{3 (2 a + a x - 6)}$

Step 4.3.2.2.2

Divide $h$ by $1$ .

$h = \frac{- 2}{3 (2 a + a x - 6)}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Move the negative in front of the fraction.

$h = - \frac{2}{3 (2 a + a x - 6)}$