Algebra Examples

$\frac{2}{3} (x - \frac{4}{5}) = - \frac{88}{15}$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (x - \frac{4}{5})) = \frac{3}{2} (- \frac{88}{15})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{3}{2} (\frac{2}{3} \cdot (x - \frac{4}{5}))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} x + \frac{2}{3} (- \frac{4}{5})) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.2

Combine $\frac{2}{3}$ and $x$ .

$\frac{3}{2} (\frac{2 x}{3} + \frac{2}{3} (- \frac{4}{5})) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.3

Multiply $\frac{2}{3} (- \frac{4}{5})$ .

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Step 2.1.1.3.1

Multiply $\frac{2}{3}$ by $\frac{4}{5}$ .

$\frac{3}{2} (\frac{2 x}{3} - \frac{2 \cdot 4}{3 \cdot 5}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.3.2

Multiply $2$ by $4$ .

$\frac{3}{2} (\frac{2 x}{3} - \frac{8}{3 \cdot 5}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.3.3

Multiply $3$ by $5$ .

$\frac{3}{2} (\frac{2 x}{3} - \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.4

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 x}{3} + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.5

Cancel the common factor of $3$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{2} (2 x) + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.6.3

Rewrite the expression.

$x + \frac{3}{2} (- \frac{8}{15}) = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Move the leading negative in $- \frac{8}{15}$ into the numerator.

$x + \frac{3}{2} \cdot \frac{- 8}{15} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.7.2

Factor $3$ out of $15$ .

$x + \frac{3}{2} \cdot \frac{- 8}{3 (5)} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.7.3

Cancel the common factor.

$x + \frac{3}{2} \cdot \frac{- 8}{3 \cdot 5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.7.4

Rewrite the expression.

$x + \frac{1}{2} \cdot \frac{- 8}{5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Factor $2$ out of $- 8$ .

$x + \frac{1}{2} \cdot \frac{2 (- 4)}{5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.8.2

Cancel the common factor.

$x + \frac{1}{2} \cdot \frac{2 \cdot - 4}{5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.8.3

Rewrite the expression.

$x + \frac{- 4}{5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.1.1.9

Move the negative in front of the fraction.

$x - \frac{4}{5} = \frac{3}{2} (- \frac{88}{15})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{3}{2} (- \frac{88}{15})$ .

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Step 2.2.1.1

Cancel the common factor of $3$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{88}{15}$ into the numerator.

$x - \frac{4}{5} = \frac{3}{2} \cdot \frac{- 88}{15}$

Step 2.2.1.1.2

Factor $3$ out of $15$ .

$x - \frac{4}{5} = \frac{3}{2} \cdot \frac{- 88}{3 (5)}$

Step 2.2.1.1.3

Cancel the common factor.

$x - \frac{4}{5} = \frac{3}{2} \cdot \frac{- 88}{3 \cdot 5}$

Step 2.2.1.1.4

Rewrite the expression.

$x - \frac{4}{5} = \frac{1}{2} \cdot \frac{- 88}{5}$

Step 2.2.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.2.1

Factor $2$ out of $- 88$ .

$x - \frac{4}{5} = \frac{1}{2} \cdot \frac{2 (- 44)}{5}$

Step 2.2.1.2.2

Cancel the common factor.

$x - \frac{4}{5} = \frac{1}{2} \cdot \frac{2 \cdot - 44}{5}$

Step 2.2.1.2.3

Rewrite the expression.

$x - \frac{4}{5} = \frac{- 44}{5}$

Step 2.2.1.3

Move the negative in front of the fraction.

$x - \frac{4}{5} = - \frac{44}{5}$

Step 3

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

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Step 3.1

Add $\frac{4}{5}$ to both sides of the equation.

$x = - \frac{44}{5} + \frac{4}{5}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 44 + 4}{5}$

Step 3.3

Add $- 44$ and $4$ .

$x = \frac{- 40}{5}$

Step 3.4

Divide $- 40$ by $5$ .

$x = - 8$