Pre-Algebra Examples

$- \frac{2}{3} = - \frac{3}{7} x - \frac{3}{5}$

Step 1

Rewrite the equation as $- \frac{3}{7} x - \frac{3}{5} = - \frac{2}{3}$ .

$- \frac{3}{7} x - \frac{3}{5} = - \frac{2}{3}$

Step 2

Simplify each term.

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Step 2.1

Combine $x$ and $\frac{3}{7}$ .

$- \frac{x \cdot 3}{7} - \frac{3}{5} = - \frac{2}{3}$

Step 2.2

Move $3$ to the left of $x$ .

$- \frac{3 x}{7} - \frac{3}{5} = - \frac{2}{3}$

Step 3

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

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Step 3.1

Add $\frac{3}{5}$ to both sides of the equation.

$- \frac{3 x}{7} = - \frac{2}{3} + \frac{3}{5}$

Step 3.2

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{3 x}{7} = - \frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5}$

Step 3.3

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{3 x}{7} = - \frac{2}{3} \cdot \frac{5}{5} + \frac{3}{5} \cdot \frac{3}{3}$

Step 3.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{2}{3}$ by $\frac{5}{5}$ .

$- \frac{3 x}{7} = - \frac{2 \cdot 5}{3 \cdot 5} + \frac{3}{5} \cdot \frac{3}{3}$

Step 3.4.2

Multiply $3$ by $5$ .

$- \frac{3 x}{7} = - \frac{2 \cdot 5}{15} + \frac{3}{5} \cdot \frac{3}{3}$

Step 3.4.3

Multiply $\frac{3}{5}$ by $\frac{3}{3}$ .

$- \frac{3 x}{7} = - \frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{5 \cdot 3}$

Step 3.4.4

Multiply $5$ by $3$ .

$- \frac{3 x}{7} = - \frac{2 \cdot 5}{15} + \frac{3 \cdot 3}{15}$

Step 3.5

Combine the numerators over the common denominator.

$- \frac{3 x}{7} = \frac{- 2 \cdot 5 + 3 \cdot 3}{15}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Multiply $- 2$ by $5$ .

$- \frac{3 x}{7} = \frac{- 10 + 3 \cdot 3}{15}$

Step 3.6.2

Multiply $3$ by $3$ .

$- \frac{3 x}{7} = \frac{- 10 + 9}{15}$

Step 3.6.3

Add $- 10$ and $9$ .

$- \frac{3 x}{7} = \frac{- 1}{15}$

Step 3.7

Move the negative in front of the fraction.

$- \frac{3 x}{7} = - \frac{1}{15}$

Step 4

Multiply both sides of the equation by $- \frac{7}{3}$ .

$- \frac{7}{3} (- \frac{3 x}{7}) = - \frac{7}{3} (- \frac{1}{15})$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{7}{3} (- \frac{3 x}{7})$ .

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Step 5.1.1.1

Cancel the common factor of $7$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{7}{3}$ into the numerator.

$\frac{- 7}{3} (- \frac{3 x}{7}) = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 x}{7}$ into the numerator.

$\frac{- 7}{3} \cdot \frac{- 3 x}{7} = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{3} \cdot \frac{- 3 x}{7} = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{3} \cdot \frac{- 3 x}{7} = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 x$ .

$\frac{- 1}{3} (3 (- x)) = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{7}{3} (- \frac{1}{15})$

Step 5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{7}{3} (- \frac{1}{15})$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- \frac{7}{3} (- \frac{1}{15})$ .

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Step 5.2.1.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{7}{3}) \frac{1}{15}$

Step 5.2.1.2

Multiply $\frac{7}{3}$ by $1$ .

$x = \frac{7}{3} \cdot \frac{1}{15}$

Step 5.2.1.3

Multiply $\frac{7}{3}$ by $\frac{1}{15}$ .

$x = \frac{7}{3 \cdot 15}$

Step 5.2.1.4

Multiply $3$ by $15$ .

$x = \frac{7}{45}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{45}$

Decimal Form:

$x = 0.1\overline{5}$