Algebra Examples

$\frac{3}{4} (x - 13) = - 2 (9 + x)$

Step 1

Simplify $\frac{3}{4} \cdot (x - 13)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{3}{4} \cdot (x - 13) = - 2 (9 + x)$

Step 1.2

Simplify by adding zeros.

$\frac{3}{4} \cdot (x - 13) = - 2 (9 + x)$

Step 1.3

Apply the distributive property.

$\frac{3}{4} x + \frac{3}{4} \cdot - 13 = - 2 (9 + x)$

Step 1.4

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + \frac{3}{4} \cdot - 13 = - 2 (9 + x)$

Step 1.5

Multiply $\frac{3}{4} \cdot - 13$ .

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Step 1.5.1

Combine $\frac{3}{4}$ and $- 13$ .

$\frac{3 x}{4} + \frac{3 \cdot - 13}{4} = - 2 (9 + x)$

Step 1.5.2

Multiply $3$ by $- 13$ .

$\frac{3 x}{4} + \frac{- 39}{4} = - 2 (9 + x)$

Step 1.6

Move the negative in front of the fraction.

$\frac{3 x}{4} - \frac{39}{4} = - 2 (9 + x)$

Step 2

Simplify $- 2 (9 + x)$ .

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Step 2.1

Apply the distributive property.

$\frac{3 x}{4} - \frac{39}{4} = - 2 \cdot 9 - 2 x$

Step 2.2

Multiply $- 2$ by $9$ .

$\frac{3 x}{4} - \frac{39}{4} = - 18 - 2 x$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $2 x$ to both sides of the equation.

$\frac{3 x}{4} - \frac{39}{4} + 2 x = - 18$

Step 3.2

To write $2 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} + 2 x \cdot \frac{4}{4} - \frac{39}{4} = - 18$

Step 3.3

Combine $2 x$ and $\frac{4}{4}$ .

$\frac{3 x}{4} + \frac{2 x \cdot 4}{4} - \frac{39}{4} = - 18$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 4}{4} - \frac{39}{4} = - 18$

Step 3.5

Combine the numerators over the common denominator.

$\frac{3 x + 2 x \cdot 4 - 39}{4} = - 18$

Step 3.6

Multiply $4$ by $2$ .

$\frac{3 x + 8 x - 39}{4} = - 18$

Step 3.7

Add $3 x$ and $8 x$ .

$\frac{11 x - 39}{4} = - 18$

Step 4

Multiply both sides by $4$ .

$\frac{11 x - 39}{4} \cdot 4 = - 18 \cdot 4$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{11 x - 39}{4} \cdot 4 = - 18 \cdot 4$

Step 5.1.1.2

Rewrite the expression.

$11 x - 39 = - 18 \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 18$ by $4$ .

$11 x - 39 = - 72$

Step 6

Solve for $x$ .

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Step 6.1

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

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Step 6.1.1

Add $39$ to both sides of the equation.

$11 x = - 72 + 39$

Step 6.1.2

Add $- 72$ and $39$ .

$11 x = - 33$

Step 6.2

Divide each term in $11 x = - 33$ by $11$ and simplify.

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Step 6.2.1

Divide each term in $11 x = - 33$ by $11$ .

$\frac{11 x}{11} = \frac{- 33}{11}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $11$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{11 x}{11} = \frac{- 33}{11}$

Step 6.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 33}{11}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Divide $- 33$ by $11$ .

$x = - 3$