Algebra Examples

$\frac{2}{3} z - 4 + z = 5 + \frac{2}{3} (z - 6)$

Step 1

Simplify $\frac{2}{3} z - 4 + z$ .

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Step 1.1

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

$\frac{2 z}{3} - 4 + z = 5 + \frac{2}{3} \cdot (z - 6)$

Step 1.2

To write $z$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 z}{3} + z \cdot \frac{3}{3} - 4 = 5 + \frac{2}{3} \cdot (z - 6)$

Step 1.3

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

$\frac{2 z}{3} + \frac{z \cdot 3}{3} - 4 = 5 + \frac{2}{3} \cdot (z - 6)$

Step 1.4

Combine the numerators over the common denominator.

$\frac{2 z + z \cdot 3}{3} - 4 = 5 + \frac{2}{3} \cdot (z - 6)$

Step 1.5

Add $2 z$ and $z \cdot 3$ .

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Step 1.5.1

Reorder $z$ and $3$ .

$\frac{2 z + 3 \cdot z}{3} - 4 = 5 + \frac{2}{3} \cdot (z - 6)$

Step 1.5.2

Add $2 z$ and $3 \cdot z$ .

$\frac{5 z}{3} - 4 = 5 + \frac{2}{3} \cdot (z - 6)$

Step 2

Simplify $5 + \frac{2}{3} \cdot (z - 6)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$\frac{5 z}{3} - 4 = 5 + \frac{2}{3} z + \frac{2}{3} \cdot - 6$

Step 2.1.2

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

$\frac{5 z}{3} - 4 = 5 + \frac{2 z}{3} + \frac{2}{3} \cdot - 6$

Step 2.1.3

Cancel the common factor of $3$ .

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Step 2.1.3.1

Factor $3$ out of $- 6$ .

$\frac{5 z}{3} - 4 = 5 + \frac{2 z}{3} + \frac{2}{3} \cdot (3 (- 2))$

Step 2.1.3.2

Cancel the common factor.

$\frac{5 z}{3} - 4 = 5 + \frac{2 z}{3} + \frac{2}{3} \cdot (3 \cdot - 2)$

Step 2.1.3.3

Rewrite the expression.

$\frac{5 z}{3} - 4 = 5 + \frac{2 z}{3} + 2 \cdot - 2$

Step 2.1.4

Multiply $2$ by $- 2$ .

$\frac{5 z}{3} - 4 = 5 + \frac{2 z}{3} - 4$

Step 2.2

Subtract $4$ from $5$ .

$\frac{5 z}{3} - 4 = \frac{2 z}{3} + 1$

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.

$\frac{5 z}{3} - 4 - \frac{2 z}{3} = 1$

Step 3.2

Combine the numerators over the common denominator.

$- 4 + \frac{5 z - 2 z}{3} = 1$

Step 3.3

Subtract $2 z$ from $5 z$ .

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

Step 3.4

Cancel the common factor of $3$ .

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Step 3.4.1

Cancel the common factor.

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

Step 3.4.2

Divide $z$ by $1$ .

$- 4 + z = 1$

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.

$z = 1 + 4$

Step 4.2

Add $1$ and $4$ .

$z = 5$