Solve for x 3/4x-1/2=-2

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

Step 1

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

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

Step 2

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

Add $\frac{1}{2}$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 2$ by $2$ .

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

Add $- 4$ and $1$ .

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

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $3 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

Cancel the common factor of $2$ .

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

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 2 \cdot - 1$

Multiply $2$ by $- 1$ .

$x = - 2$

Solve for x 3/4x-1/2=-2

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