Algebra Examples

$\frac{3}{2} (x + \frac{4}{3}) = - \frac{11}{2}$

Step 1

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

$\frac{2}{3} (\frac{3}{2} \cdot (x + \frac{4}{3})) = \frac{2}{3} (- \frac{11}{2})$

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 $\frac{2}{3} (\frac{3}{2} \cdot (x + \frac{4}{3}))$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{2}{3} (\frac{3}{2} x + \frac{3}{2} \cdot \frac{4}{3}) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.2

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

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot \frac{4}{3}) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Cancel the common factor.

$\frac{2}{3} (\frac{3 x}{2} + \frac{3}{2} \cdot \frac{4}{3}) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.3.2

Rewrite the expression.

$\frac{2}{3} (\frac{3 x}{2} + \frac{1}{2} \cdot 4) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.4

Cancel the common factor of $2$ .

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Step 2.1.1.4.1

Factor $2$ out of $4$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{1}{2} \cdot (2 (2))) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.4.2

Cancel the common factor.

$\frac{2}{3} (\frac{3 x}{2} + \frac{1}{2} \cdot (2 \cdot 2)) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.4.3

Rewrite the expression.

$\frac{2}{3} (\frac{3 x}{2} + 2) = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.5

Apply the distributive property.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.6.2

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.7

Cancel the common factor of $3$ .

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Step 2.1.1.7.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.7.2

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.7.3

Rewrite the expression.

$x + \frac{2}{3} \cdot 2 = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.8

Multiply $\frac{2}{3} \cdot 2$ .

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Step 2.1.1.8.1

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

$x + \frac{2 \cdot 2}{3} = \frac{2}{3} (- \frac{11}{2})$

Step 2.1.1.8.2

Multiply $2$ by $2$ .

$x + \frac{4}{3} = \frac{2}{3} (- \frac{11}{2})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{2}{3} (- \frac{11}{2})$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Move the leading negative in $- \frac{11}{2}$ into the numerator.

$x + \frac{4}{3} = \frac{2}{3} \cdot \frac{- 11}{2}$

Step 2.2.1.1.2

Cancel the common factor.

$x + \frac{4}{3} = \frac{2}{3} \cdot \frac{- 11}{2}$

Step 2.2.1.1.3

Rewrite the expression.

$x + \frac{4}{3} = \frac{1}{3} \cdot - 11$

Step 2.2.1.2

Combine $\frac{1}{3}$ and $- 11$ .

$x + \frac{4}{3} = \frac{- 11}{3}$

Step 2.2.1.3

Move the negative in front of the fraction.

$x + \frac{4}{3} = - \frac{11}{3}$

Step 3

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

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Step 3.1

Subtract $\frac{4}{3}$ from both sides of the equation.

$x = - \frac{11}{3} - \frac{4}{3}$

Step 3.2

Combine the numerators over the common denominator.

$x = \frac{- 11 - 4}{3}$

Step 3.3

Subtract $4$ from $- 11$ .

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

Step 3.4

Divide $- 15$ by $3$ .

$x = - 5$