Algebra Examples

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

Step 1

Simplify $\frac{2 z - 3}{5} - \frac{z - 6}{4}$ .

Tap for more steps...

Step 1.1

To write $\frac{2 z - 3}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Step 1.2

To write $- \frac{z - 6}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{2 z - 3}{5}$ by $\frac{4}{4}$ .

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

Step 1.3.2

Multiply $5$ by $4$ .

$\frac{(2 z - 3) \cdot 4}{20} - \frac{z - 6}{4} \cdot \frac{5}{5} = 3$

Step 1.3.3

Multiply $\frac{z - 6}{4}$ by $\frac{5}{5}$ .

$\frac{(2 z - 3) \cdot 4}{20} - \frac{(z - 6) \cdot 5}{4 \cdot 5} = 3$

Step 1.3.4

Multiply $4$ by $5$ .

$\frac{(2 z - 3) \cdot 4}{20} - \frac{(z - 6) \cdot 5}{20} = 3$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(2 z - 3) \cdot 4 - (z - 6) \cdot 5}{20} = 3$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$\frac{2 z \cdot 4 - 3 \cdot 4 - (z - 6) \cdot 5}{20} = 3$

Step 1.5.2

Multiply $4$ by $2$ .

$\frac{8 z - 3 \cdot 4 - (z - 6) \cdot 5}{20} = 3$

Step 1.5.3

Multiply $- 3$ by $4$ .

$\frac{8 z - 12 - (z - 6) \cdot 5}{20} = 3$

Step 1.5.4

Apply the distributive property.

$\frac{8 z - 12 + (- z - - 6) \cdot 5}{20} = 3$

Step 1.5.5

Multiply $- 1$ by $- 6$ .

$\frac{8 z - 12 + (- z + 6) \cdot 5}{20} = 3$

Step 1.5.6

Apply the distributive property.

$\frac{8 z - 12 - z \cdot 5 + 6 \cdot 5}{20} = 3$

Step 1.5.7

Multiply $5$ by $- 1$ .

$\frac{8 z - 12 - 5 z + 6 \cdot 5}{20} = 3$

Step 1.5.8

Multiply $6$ by $5$ .

$\frac{8 z - 12 - 5 z + 30}{20} = 3$

Step 1.5.9

Subtract $5 z$ from $8 z$ .

$\frac{3 z - 12 + 30}{20} = 3$

Step 1.5.10

Add $- 12$ and $30$ .

$\frac{3 z + 18}{20} = 3$

Step 1.5.11

Factor $3$ out of $3 z + 18$ .

Tap for more steps...

Step 1.5.11.1

Factor $3$ out of $3 z$ .

$\frac{3 (z) + 18}{20} = 3$

Step 1.5.11.2

Factor $3$ out of $18$ .

$\frac{3 z + 3 \cdot 6}{20} = 3$

Step 1.5.11.3

Factor $3$ out of $3 z + 3 \cdot 6$ .

$\frac{3 (z + 6)}{20} = 3$

Step 2

Multiply both sides of the equation by $\frac{20}{3}$ .

$\frac{20}{3} \cdot \frac{3 (z + 6)}{20} = \frac{20}{3} \cdot 3$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{20}{3} \cdot \frac{3 (z + 6)}{20}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $20$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{20}{3} \cdot \frac{3 (z + 6)}{20} = \frac{20}{3} \cdot 3$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 (z + 6)) = \frac{20}{3} \cdot 3$

Step 3.1.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.2.1

Cancel the common factor.

$\frac{1}{3} (3 (z + 6)) = \frac{20}{3} \cdot 3$

Step 3.1.1.2.2

Rewrite the expression.

$z + 6 = \frac{20}{3} \cdot 3$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$z + 6 = \frac{20}{3} \cdot 3$

Step 3.2.1.2

Rewrite the expression.

$z + 6 = 20$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $6$ from both sides of the equation.

$z = 20 - 6$

Step 4.2

Subtract $6$ from $20$ .

$z = 14$