Pre-Algebra Examples

$\frac{3}{8} x + 14 = \frac{5}{8} x - 2$

Step 1

Combine $\frac{3}{8}$ and $x$ .

$\frac{3 x}{8} + 14 = \frac{5}{8} x - 2$

Step 2

Combine $\frac{5}{8}$ and $x$ .

$\frac{3 x}{8} + 14 = \frac{5 x}{8} - 2$

Step 3

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

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Step 3.1

Subtract $\frac{5 x}{8}$ from both sides of the equation.

$\frac{3 x}{8} + 14 - \frac{5 x}{8} = - 2$

Step 3.2

Combine the numerators over the common denominator.

$14 + \frac{3 x - 5 x}{8} = - 2$

Step 3.3

Subtract $5 x$ from $3 x$ .

$14 + \frac{- 2 x}{8} = - 2$

Step 3.4

Simplify each term.

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Step 3.4.1

Cancel the common factor of $- 2$ and $8$ .

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Step 3.4.1.1

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

$14 + \frac{2 (- x)}{8} = - 2$

Step 3.4.1.2

Cancel the common factors.

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Step 3.4.1.2.1

Factor $2$ out of $8$ .

$14 + \frac{2 (- x)}{2 (4)} = - 2$

Step 3.4.1.2.2

Cancel the common factor.

$14 + \frac{2 (- x)}{2 \cdot 4} = - 2$

Step 3.4.1.2.3

Rewrite the expression.

$14 + \frac{- x}{4} = - 2$

Step 3.4.2

Move the negative in front of the fraction.

$14 - \frac{x}{4} = - 2$

Step 4

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

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Step 4.1

Subtract $14$ from both sides of the equation.

$- \frac{x}{4} = - 2 - 14$

Step 4.2

Subtract $14$ from $- 2$ .

$- \frac{x}{4} = - 16$

Step 5

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{x}{4}) = - 4 \cdot - 16$

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 $- 4 (- \frac{x}{4})$ .

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Step 6.1.1.1

Cancel the common factor of $4$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{x}{4}$ into the numerator.

$- 4 \frac{- x}{4} = - 4 \cdot - 16$

Step 6.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- x}{4} = - 4 \cdot - 16$

Step 6.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- x}{4} = - 4 \cdot - 16$

Step 6.1.1.1.4

Rewrite the expression.

$- - x = - 4 \cdot - 16$

Step 6.1.1.2

Multiply.

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Step 6.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 4 \cdot - 16$

Step 6.1.1.2.2

Multiply $x$ by $1$ .

$x = - 4 \cdot - 16$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $- 4$ by $- 16$ .

$x = 64$