Algebra Examples

$\frac{5}{3} z + 1 = 3 - \frac{2}{3} Z$

Step 1

Combine $\frac{5}{3}$ and $z$ .

$\frac{5 z}{3} + 1 = 3 - \frac{2}{3} Z$

Step 2

Simplify each term.

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Step 2.1

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

$\frac{5 z}{3} + 1 = 3 - \frac{Z \cdot 2}{3}$

Step 2.2

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

$\frac{5 z}{3} + 1 = 3 - \frac{2 Z}{3}$

Step 3

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

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Step 3.1

Subtract $1$ from both sides of the equation.

$\frac{5 z}{3} = 3 - \frac{2 Z}{3} - 1$

Step 3.2

Subtract $1$ from $3$ .

$\frac{5 z}{3} = - \frac{2 Z}{3} + 2$

Step 4

Multiply both sides of the equation by $\frac{3}{5}$ .

$\frac{3}{5} \cdot \frac{5 z}{3} = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

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 $\frac{3}{5} \cdot \frac{5 z}{3}$ .

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Step 5.1.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1.1

Cancel the common factor.

$\frac{3}{5} \cdot \frac{5 z}{3} = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

Step 5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 z) = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

Step 5.1.1.2

Cancel the common factor of $5$ .

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Step 5.1.1.2.1

Factor $5$ out of $5 z$ .

$\frac{1}{5} (5 (z)) = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 z) = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

Step 5.1.1.2.3

Rewrite the expression.

$z = \frac{3}{5} (- \frac{2 Z}{3} + 2)$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $\frac{3}{5} (- \frac{2 Z}{3} + 2)$ .

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Step 5.2.1.1

Apply the distributive property.

$z = \frac{3}{5} (- \frac{2 Z}{3}) + \frac{3}{5} \cdot 2$

Step 5.2.1.2

Cancel the common factor of $3$ .

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Step 5.2.1.2.1

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

$z = \frac{3}{5} \cdot \frac{- 2 Z}{3} + \frac{3}{5} \cdot 2$

Step 5.2.1.2.2

Cancel the common factor.

$z = \frac{3}{5} \cdot \frac{- 2 Z}{3} + \frac{3}{5} \cdot 2$

Step 5.2.1.2.3

Rewrite the expression.

$z = \frac{1}{5} (- 2 Z) + \frac{3}{5} \cdot 2$

Step 5.2.1.3

Combine $- 2$ and $\frac{1}{5}$ .

$z = \frac{- 2}{5} Z + \frac{3}{5} \cdot 2$

Step 5.2.1.4

Combine $\frac{- 2}{5}$ and $Z$ .

$z = \frac{- 2 Z}{5} + \frac{3}{5} \cdot 2$

Step 5.2.1.5

Multiply $\frac{3}{5} \cdot 2$ .

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Step 5.2.1.5.1

Combine $\frac{3}{5}$ and $2$ .

$z = \frac{- 2 Z}{5} + \frac{3 \cdot 2}{5}$

Step 5.2.1.5.2

Multiply $3$ by $2$ .

$z = \frac{- 2 Z}{5} + \frac{6}{5}$

Step 5.2.1.6

Move the negative in front of the fraction.

$z = - \frac{2 Z}{5} + \frac{6}{5}$