Solve for z 3/4-1/3z=1/4

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

Combine $z$ and $\frac{1}{3}$ .

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

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

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Subtract $\frac{3}{4}$ from both sides of the equation.

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $1$ .

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

Cancel the common factor of $- 2$ and $4$ .

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Factor $2$ out of $- 2$ .

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

Cancel the common factors.

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Factor $2$ out of $4$ .

$- \frac{z}{3} = \frac{2 \cdot - 1}{2 \cdot 2}$

Cancel the common factor.

$- \frac{z}{3} = \frac{2 \cdot - 1}{2 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 3$ .

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

Simplify both sides of the equation.

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Simplify $- 3 \cdot (- \frac{z}{3})$ .

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Cancel the common factor of $3$ .

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

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

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Multiply $- 1$ by $- 1$ .

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

Multiply $z$ by $1$ .

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

Multiply $- 3 (- \frac{1}{2})$ .

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Multiply $- 1$ by $- 3$ .

$z = 3 (\frac{1}{2})$

Combine $3$ and $\frac{1}{2}$ .

$z = \frac{3}{2}$

The result can be shown in multiple forms.

Exact Form:

$z = \frac{3}{2}$

Decimal Form:

$z = 1.5$

Mixed Number Form:

$z = 1 \frac{1}{2}$

Solve for z 3/4-1/3z=1/4

Solving MATH problems