Pre-Algebra Examples

$\frac{3}{8} - x = \frac{2}{3}$

Step 1

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

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Step 1.1

Subtract $\frac{3}{8}$ from both sides of the equation.

$- x = \frac{2}{3} - \frac{3}{8}$

Step 1.2

To write $\frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- x = \frac{2}{3} \cdot \frac{8}{8} - \frac{3}{8}$

Step 1.3

To write $- \frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- x = \frac{2}{3} \cdot \frac{8}{8} - \frac{3}{8} \cdot \frac{3}{3}$

Step 1.4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$- x = \frac{2 \cdot 8}{3 \cdot 8} - \frac{3}{8} \cdot \frac{3}{3}$

Step 1.4.2

Multiply $3$ by $8$ .

$- x = \frac{2 \cdot 8}{24} - \frac{3}{8} \cdot \frac{3}{3}$

Step 1.4.3

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$- x = \frac{2 \cdot 8}{24} - \frac{3 \cdot 3}{8 \cdot 3}$

Step 1.4.4

Multiply $8$ by $3$ .

$- x = \frac{2 \cdot 8}{24} - \frac{3 \cdot 3}{24}$

Step 1.5

Combine the numerators over the common denominator.

$- x = \frac{2 \cdot 8 - 3 \cdot 3}{24}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $2$ by $8$ .

$- x = \frac{16 - 3 \cdot 3}{24}$

Step 1.6.2

Multiply $- 3$ by $3$ .

$- x = \frac{16 - 9}{24}$

Step 1.6.3

Subtract $9$ from $16$ .

$- x = \frac{7}{24}$

Step 2

Divide each term in $- x = \frac{7}{24}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- x = \frac{7}{24}$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\frac{7}{24}}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\frac{7}{24}}{- 1}$

Step 2.2.2

Divide $x$ by $1$ .

$x = \frac{\frac{7}{24}}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative one from the denominator of $\frac{\frac{7}{24}}{- 1}$ .

$x = - 1 \cdot \frac{7}{24}$

Step 2.3.2

Rewrite $- 1 \cdot \frac{7}{24}$ as $- \frac{7}{24}$ .

$x = - \frac{7}{24}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{24}$

Decimal Form:

$x = - 0.291\overline{6}$