Pre-Algebra Examples

$9 + \frac{3}{4} x = \frac{7}{8} x - 10$

Step 1

Combine $\frac{3}{4}$ and $x$ .

$9 + \frac{3 x}{4} = \frac{7}{8} x - 10$

Step 2

Combine $\frac{7}{8}$ and $x$ .

$9 + \frac{3 x}{4} = \frac{7 x}{8} - 10$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $\frac{7 x}{8}$ from both sides of the equation.

$9 + \frac{3 x}{4} - \frac{7 x}{8} = - 10$

Step 3.2

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 + \frac{3 x}{4} \cdot \frac{2}{2} - \frac{7 x}{8} = - 10$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{3 x}{4}$ by $\frac{2}{2}$ .

$9 + \frac{3 x \cdot 2}{4 \cdot 2} - \frac{7 x}{8} = - 10$

Step 3.3.2

Multiply $4$ by $2$ .

$9 + \frac{3 x \cdot 2}{8} - \frac{7 x}{8} = - 10$

Step 3.4

Combine the numerators over the common denominator.

$9 + \frac{3 x \cdot 2 - 7 x}{8} = - 10$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $3 x \cdot 2 - 7 x$ .

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Step 3.5.1.1.1

Factor $x$ out of $3 x \cdot 2$ .

$9 + \frac{x (3 \cdot 2) - 7 x}{8} = - 10$

Step 3.5.1.1.2

Factor $x$ out of $- 7 x$ .

$9 + \frac{x (3 \cdot 2) + x \cdot - 7}{8} = - 10$

Step 3.5.1.1.3

Factor $x$ out of $x (3 \cdot 2) + x \cdot - 7$ .

$9 + \frac{x (3 \cdot 2 - 7)}{8} = - 10$

Step 3.5.1.2

Multiply $3$ by $2$ .

$9 + \frac{x (6 - 7)}{8} = - 10$

Step 3.5.1.3

Subtract $7$ from $6$ .

$9 + \frac{x \cdot - 1}{8} = - 10$

Step 3.5.2

Move $- 1$ to the left of $x$ .

$9 + \frac{- 1 \cdot x}{8} = - 10$

Step 3.5.3

Move the negative in front of the fraction.

$9 - \frac{x}{8} = - 10$

Step 4

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

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Step 4.1

Subtract $9$ from both sides of the equation.

$- \frac{x}{8} = - 10 - 9$

Step 4.2

Subtract $9$ from $- 10$ .

$- \frac{x}{8} = - 19$

Step 5

Multiply both sides of the equation by $- 8$ .

$- 8 (- \frac{x}{8}) = - 8 \cdot - 19$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $- 8 (- \frac{x}{8})$ .

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Step 6.1.1.1

Cancel the common factor of $8$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{8}$ into the numerator.

$- 8 \frac{- x}{8} = - 8 \cdot - 19$

Step 6.1.1.1.2

Factor $8$ out of $- 8$ .

$8 (- 1) \frac{- x}{8} = - 8 \cdot - 19$

Step 6.1.1.1.3

Cancel the common factor.

$8 \cdot - 1 \frac{- x}{8} = - 8 \cdot - 19$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 8 \cdot - 19$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 8 \cdot - 19$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 8 \cdot - 19$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 8$ by $- 19$ .

$x = 152$