Solve for z -5/2=3/4z+1/2

$- \frac{5}{2} = \frac{3}{4} z + \frac{1}{2}$

Rewrite the equation as $\frac{3}{4} z + \frac{1}{2} = - \frac{5}{2}$ .

$\frac{3}{4} z + \frac{1}{2} = - \frac{5}{2}$

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

$\frac{3 z}{4} + \frac{1}{2} = - \frac{5}{2}$

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

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Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{3 z}{4} = - \frac{5}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{3 z}{4} = \frac{- 5 - 1}{2}$

Subtract $1$ from $- 5$ .

$\frac{3 z}{4} = \frac{- 6}{2}$

Divide $- 6$ by $2$ .

$\frac{3 z}{4} = - 3$

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

$\frac{4}{3} \cdot \frac{3 z}{4} = \frac{4}{3} \cdot - 3$

Simplify both sides of the equation.

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

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Cancel the common factor of $4$ .

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Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 z}{4} = \frac{4}{3} \cdot - 3$

Rewrite the expression.

$\frac{1}{3} \cdot (3 z) = \frac{4}{3} \cdot - 3$

Cancel the common factor of $3$ .

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Factor $3$ out of $3 z$ .

$\frac{1}{3} \cdot (3 (z)) = \frac{4}{3} \cdot - 3$

Cancel the common factor.

$\frac{1}{3} \cdot (3 z) = \frac{4}{3} \cdot - 3$

Rewrite the expression.

$z = \frac{4}{3} \cdot - 3$

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

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Cancel the common factor of $3$ .

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Factor $3$ out of $- 3$ .

$z = \frac{4}{3} \cdot (3 (- 1))$

Cancel the common factor.

$z = \frac{4}{3} \cdot (3 \cdot - 1)$

Rewrite the expression.

$z = 4 \cdot - 1$

Multiply $4$ by $- 1$ .

$z = - 4$

Solve for z -5/2=3/4z+1/2

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