Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Subtract $\frac{5}{4}$ from both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Subtract $5$ from $- 1$ .

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

Step 2.4

Cancel the common factor of $- 6$ and $4$ .

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Step 2.4.1

Factor $2$ out of $- 6$ .

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

Step 2.4.2

Cancel the common factors.

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Step 2.4.2.1

Factor $2$ out of $4$ .

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

Step 2.4.2.2

Cancel the common factor.

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

Step 2.4.2.3

Rewrite the expression.

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

Step 2.5

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $3$ .

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Step 4.1.1.2.1

Factor $3$ out of $3 z$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

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

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

Step 4.2.1.1.2

Factor $2$ out of $4$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

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

Step 4.2.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.2.1

Factor $3$ out of $- 3$ .

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

Step 4.2.1.2.2

Cancel the common factor.

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

Step 4.2.1.2.3

Rewrite the expression.

$z = 2 \cdot - 1$

Step 4.2.1.3

Multiply $2$ by $- 1$ .

$z = - 2$