Pre-Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

Move $2$ to the left of $z$ .

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

Step 2

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

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

Step 3

Move all terms containing $z$ to the left side of the equation.

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Step 3.1

Subtract $\frac{2 z}{3}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $2 z$ from $- 2 z$ .

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

Step 3.4

Move the negative in front of the fraction.

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

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

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

Step 4.2

Add $4$ and $4$ .

$- \frac{4 z}{3} = 8$

Step 5

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

$- \frac{3}{4} (- \frac{4 z}{3}) = - \frac{3}{4} \cdot 8$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Cancel the common factor of $3$ .

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Step 6.1.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$\frac{- 3}{4} (- \frac{4 z}{3}) = - \frac{3}{4} \cdot 8$

Step 6.1.1.1.2

Move the leading negative in $- \frac{4 z}{3}$ into the numerator.

$\frac{- 3}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot 8$

Step 6.1.1.1.3

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot 8$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{3 \cdot - 1}{4} \cdot \frac{- 4 z}{3} = - \frac{3}{4} \cdot 8$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{4} (- 4 z) = - \frac{3}{4} \cdot 8$

Step 6.1.1.2

Cancel the common factor of $4$ .

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Step 6.1.1.2.1

Factor $4$ out of $- 4 z$ .

$\frac{- 1}{4} (4 (- z)) = - \frac{3}{4} \cdot 8$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{4} (4 (- z)) = - \frac{3}{4} \cdot 8$

Step 6.1.1.2.3

Rewrite the expression.

$- - z = - \frac{3}{4} \cdot 8$

Step 6.1.1.3

Multiply.

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Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 z = - \frac{3}{4} \cdot 8$

Step 6.1.1.3.2

Multiply $z$ by $1$ .

$z = - \frac{3}{4} \cdot 8$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $- \frac{3}{4} \cdot 8$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$z = \frac{- 3}{4} \cdot 8$

Step 6.2.1.1.2

Factor $4$ out of $8$ .

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

Step 6.2.1.1.3

Cancel the common factor.

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

Step 6.2.1.1.4

Rewrite the expression.

$z = - 3 \cdot 2$

Step 6.2.1.2

Multiply $- 3$ by $2$ .

$z = - 6$