Algebra Examples

$- \frac{3}{4} (x + 2) = 6$

Step 1

Multiply both sides of the equation by $- \frac{4}{3}$ .

$- \frac{4}{3} (- \frac{3}{4} \cdot (x + 2)) = - \frac{4}{3} \cdot 6$

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

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Step 2.1.1.1

Simplify terms.

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Step 2.1.1.1.1

Apply the distributive property.

$- \frac{4}{3} (- \frac{3}{4} x - \frac{3}{4} \cdot 2) = - \frac{4}{3} \cdot 6$

Step 2.1.1.1.2

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

$- \frac{4}{3} (- \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 2) = - \frac{4}{3} \cdot 6$

Step 2.1.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.1.3.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$- \frac{4}{3} (- \frac{x \cdot 3}{4} + \frac{- 3}{4} \cdot 2) = - \frac{4}{3} \cdot 6$

Step 2.1.1.1.3.2

Factor $2$ out of $4$ .

$- \frac{4}{3} (- \frac{x \cdot 3}{4} + \frac{- 3}{2 (2)} \cdot 2) = - \frac{4}{3} \cdot 6$

Step 2.1.1.1.3.3

Cancel the common factor.

$- \frac{4}{3} (- \frac{x \cdot 3}{4} + \frac{- 3}{2 \cdot 2} \cdot 2) = - \frac{4}{3} \cdot 6$

Step 2.1.1.1.3.4

Rewrite the expression.

$- \frac{4}{3} (- \frac{x \cdot 3}{4} + \frac{- 3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.2

Simplify each term.

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Step 2.1.1.2.1

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

$- \frac{4}{3} (- \frac{3 \cdot x}{4} + \frac{- 3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.2.2

Move the negative in front of the fraction.

$- \frac{4}{3} (- \frac{3 x}{4} - \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3

Simplify terms.

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Step 2.1.1.3.1

Apply the distributive property.

$- \frac{4}{3} (- \frac{3 x}{4}) - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.2

Cancel the common factor of $4$ .

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Step 2.1.1.3.2.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$\frac{- 4}{3} (- \frac{3 x}{4}) - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.2.2

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$\frac{- 4}{3} \cdot \frac{- 3 x}{4} - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.2.3

Factor $4$ out of $- 4$ .

$\frac{4 (- 1)}{3} \cdot \frac{- 3 x}{4} - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.2.4

Cancel the common factor.

$\frac{4 \cdot - 1}{3} \cdot \frac{- 3 x}{4} - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.2.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 x) - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.3.1

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

$\frac{- 1}{3} (3 (- x)) - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.3.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- x)) - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.3.3

Rewrite the expression.

$- - x - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.4

Multiply.

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Step 2.1.1.3.4.1

Multiply $- 1$ by $- 1$ .

$1 x - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.4.2

Multiply $x$ by $1$ .

$x - \frac{4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.5

Cancel the common factor of $2$ .

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Step 2.1.1.3.5.1

Move the leading negative in $- \frac{4}{3}$ into the numerator.

$x + \frac{- 4}{3} (- \frac{3}{2}) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.5.2

Move the leading negative in $- \frac{3}{2}$ into the numerator.

$x + \frac{- 4}{3} \cdot \frac{- 3}{2} = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.5.3

Factor $2$ out of $- 4$ .

$x + \frac{2 (- 2)}{3} \cdot \frac{- 3}{2} = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.5.4

Cancel the common factor.

$x + \frac{2 \cdot - 2}{3} \cdot \frac{- 3}{2} = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.5.5

Rewrite the expression.

$x + \frac{- 2}{3} \cdot - 3 = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.6

Cancel the common factor of $3$ .

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Step 2.1.1.3.6.1

Factor $3$ out of $- 3$ .

$x + \frac{- 2}{3} \cdot (3 (- 1)) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.6.2

Cancel the common factor.

$x + \frac{- 2}{3} \cdot (3 \cdot - 1) = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.6.3

Rewrite the expression.

$x - 2 \cdot - 1 = - \frac{4}{3} \cdot 6$

Step 2.1.1.3.7

Multiply $- 2$ by $- 1$ .

$x + 2 = - \frac{4}{3} \cdot 6$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{4}{3} \cdot 6$ .

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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 $- \frac{4}{3}$ into the numerator.

$x + 2 = \frac{- 4}{3} \cdot 6$

Step 2.2.1.1.2

Factor $3$ out of $6$ .

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

Step 2.2.1.1.3

Cancel the common factor.

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

Step 2.2.1.1.4

Rewrite the expression.

$x + 2 = - 4 \cdot 2$

Step 2.2.1.2

Multiply $- 4$ by $2$ .

$x + 2 = - 8$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the equation.

$x = - 8 - 2$

Step 3.2

Subtract $2$ from $- 8$ .

$x = - 10$