Algebra Examples

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

Step 1

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

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

Step 3.2

Add $5$ and $3$ .

$- \frac{z}{4} = 8$

Step 4

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{z}{4}) = - 4 \cdot 8$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 4 (- \frac{z}{4})$ .

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Step 5.1.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1.1

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

$- 4 \frac{- z}{4} = - 4 \cdot 8$

Step 5.1.1.1.2

Factor $4$ out of $- 4$ .

$4 (- 1) \frac{- z}{4} = - 4 \cdot 8$

Step 5.1.1.1.3

Cancel the common factor.

$4 \cdot - 1 \frac{- z}{4} = - 4 \cdot 8$

Step 5.1.1.1.4

Rewrite the expression.

$- - z = - 4 \cdot 8$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 z = - 4 \cdot 8$

Step 5.1.1.2.2

Multiply $z$ by $1$ .

$z = - 4 \cdot 8$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 4$ by $8$ .

$z = - 32$