Algebra Examples

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

Step 1

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

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

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 $\frac{2}{3} (\frac{3}{2} \cdot (x + \frac{3}{5}))$ .

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Step 2.1.1.1

Apply the distributive property.

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

Step 2.1.1.2

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

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

Step 2.1.1.3

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

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Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Multiply $3$ by $3$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{9}{2 \cdot 5}) = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.3.3

Multiply $2$ by $5$ .

$\frac{2}{3} (\frac{3 x}{2} + \frac{9}{10}) = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.4

Apply the distributive property.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.5

Cancel the common factor of $2$ .

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Step 2.1.1.5.1

Cancel the common factor.

$\frac{2}{3} \cdot \frac{3 x}{2} + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.5.2

Rewrite the expression.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.6

Cancel the common factor of $3$ .

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Step 2.1.1.6.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.6.2

Cancel the common factor.

$\frac{1}{3} (3 x) + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.6.3

Rewrite the expression.

$x + \frac{2}{3} \cdot \frac{9}{10} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.7

Cancel the common factor of $2$ .

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Step 2.1.1.7.1

Factor $2$ out of $10$ .

$x + \frac{2}{3} \cdot \frac{9}{2 (5)} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.7.2

Cancel the common factor.

$x + \frac{2}{3} \cdot \frac{9}{2 \cdot 5} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.7.3

Rewrite the expression.

$x + \frac{1}{3} \cdot \frac{9}{5} = \frac{2}{3} (- \frac{3}{5})$

Step 2.1.1.8

Cancel the common factor of $3$ .

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Step 2.1.1.8.1

Factor $3$ out of $9$ .

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

Step 2.1.1.8.2

Cancel the common factor.

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

Step 2.1.1.8.3

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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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 $- \frac{3}{5}$ into the numerator.

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

Step 2.2.1.1.2

Factor $3$ out of $- 3$ .

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

Step 2.2.1.1.3

Cancel the common factor.

$x + \frac{3}{5} = \frac{2}{3} \cdot \frac{3 \cdot - 1}{5}$

Step 2.2.1.1.4

Rewrite the expression.

$x + \frac{3}{5} = 2 (\frac{- 1}{5})$

Step 2.2.1.2

Combine $2$ and $\frac{- 1}{5}$ .

$x + \frac{3}{5} = \frac{2 \cdot - 1}{5}$

Step 2.2.1.3

Simplify the expression.

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Step 2.2.1.3.1

Multiply $2$ by $- 1$ .

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

Step 2.2.1.3.2

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

Subtract $\frac{3}{5}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $3$ from $- 2$ .

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

Step 3.4

Divide $- 5$ by $5$ .

$x = - 1$