Basic Math Examples

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

Step 1

Rewrite the equation as $\frac{3}{4} z + 4 = y$ .

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

Step 2

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

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

Step 3

Subtract $4$ from both sides of the equation.

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

Step 4

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

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

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

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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

Cancel the common factor.

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

Step 5.1.1.1.2

Rewrite the expression.

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

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $3 z$ .

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

Step 5.1.1.2.2

Cancel the common factor.

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

Step 5.1.1.2.3

Rewrite the expression.

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

Step 5.2

Simplify the right side.

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Step 5.2.1

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

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Step 5.2.1.1

Apply the distributive property.

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

Step 5.2.1.2

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

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

Step 5.2.1.3

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

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Step 5.2.1.3.1

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

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

Step 5.2.1.3.2

Multiply $4$ by $- 4$ .

$z = \frac{4 y}{3} + \frac{- 16}{3}$

Step 5.2.1.4

Move the negative in front of the fraction.

$z = \frac{4 y}{3} - \frac{16}{3}$