Basic Math Examples

$\frac{4 z}{5} + \frac{1}{5} + 9 = \frac{5 z}{6} - \frac{7}{5}$

Step 1

Simplify $\frac{4 z}{5} + \frac{1}{5} + 9$ .

Tap for more steps...

Step 1.1

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{4 z}{5} + \frac{1}{5} + 9 \cdot \frac{5}{5} = \frac{5 z}{6} - \frac{7}{5}$

Step 1.2

Combine $9$ and $\frac{5}{5}$ .

$\frac{4 z}{5} + \frac{1}{5} + \frac{9 \cdot 5}{5} = \frac{5 z}{6} - \frac{7}{5}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{4 z}{5} + \frac{1 + 9 \cdot 5}{5} = \frac{5 z}{6} - \frac{7}{5}$

Step 1.4

Simplify the numerator.

Tap for more steps...

Step 1.4.1

Multiply $9$ by $5$ .

$\frac{4 z}{5} + \frac{1 + 45}{5} = \frac{5 z}{6} - \frac{7}{5}$

Step 1.4.2

Add $1$ and $45$ .

$\frac{4 z}{5} + \frac{46}{5} = \frac{5 z}{6} - \frac{7}{5}$

Step 2

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

Tap for more steps...

Step 2.1

Subtract $\frac{5 z}{6}$ from both sides of the equation.

$\frac{4 z}{5} + \frac{46}{5} - \frac{5 z}{6} = - \frac{7}{5}$

Step 2.2

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

$\frac{4 z}{5} \cdot \frac{6}{6} - \frac{5 z}{6} + \frac{46}{5} = - \frac{7}{5}$

Step 2.3

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

$\frac{4 z}{5} \cdot \frac{6}{6} - \frac{5 z}{6} \cdot \frac{5}{5} + \frac{46}{5} = - \frac{7}{5}$

Step 2.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.4.1

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

$\frac{4 z \cdot 6}{5 \cdot 6} - \frac{5 z}{6} \cdot \frac{5}{5} + \frac{46}{5} = - \frac{7}{5}$

Step 2.4.2

Multiply $5$ by $6$ .

$\frac{4 z \cdot 6}{30} - \frac{5 z}{6} \cdot \frac{5}{5} + \frac{46}{5} = - \frac{7}{5}$

Step 2.4.3

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

$\frac{4 z \cdot 6}{30} - \frac{5 z \cdot 5}{6 \cdot 5} + \frac{46}{5} = - \frac{7}{5}$

Step 2.4.4

Multiply $6$ by $5$ .

$\frac{4 z \cdot 6}{30} - \frac{5 z \cdot 5}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{4 z \cdot 6 - 5 z \cdot 5}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6

Simplify each term.

Tap for more steps...

Step 2.6.1

Simplify the numerator.

Tap for more steps...

Step 2.6.1.1

Factor $z$ out of $4 z \cdot 6 - 5 z \cdot 5$ .

Tap for more steps...

Step 2.6.1.1.1

Factor $z$ out of $4 z \cdot 6$ .

$\frac{z (4 \cdot 6) - 5 z \cdot 5}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.1.1.2

Factor $z$ out of $- 5 z \cdot 5$ .

$\frac{z (4 \cdot 6) + z (- 5 \cdot 5)}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.1.1.3

Factor $z$ out of $z (4 \cdot 6) + z (- 5 \cdot 5)$ .

$\frac{z (4 \cdot 6 - 5 \cdot 5)}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.1.2

Multiply $4$ by $6$ .

$\frac{z (24 - 5 \cdot 5)}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.1.3

Multiply $- 5$ by $5$ .

$\frac{z (24 - 25)}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.1.4

Subtract $25$ from $24$ .

$\frac{z \cdot - 1}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.2

Move $- 1$ to the left of $z$ .

$\frac{- 1 \cdot z}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 2.6.3

Move the negative in front of the fraction.

$- \frac{z}{30} + \frac{46}{5} = - \frac{7}{5}$

Step 3

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

Tap for more steps...

Step 3.1

Subtract $\frac{46}{5}$ from both sides of the equation.

$- \frac{z}{30} = - \frac{7}{5} - \frac{46}{5}$

Step 3.2

Combine the numerators over the common denominator.

$- \frac{z}{30} = \frac{- 7 - 46}{5}$

Step 3.3

Subtract $46$ from $- 7$ .

$- \frac{z}{30} = \frac{- 53}{5}$

Step 3.4

Move the negative in front of the fraction.

$- \frac{z}{30} = - \frac{53}{5}$

Step 4

Multiply both sides of the equation by $- 30$ .

$- 30 (- \frac{z}{30}) = - 30 (- \frac{53}{5})$

Step 5

Simplify both sides of the equation.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

Simplify $- 30 (- \frac{z}{30})$ .

Tap for more steps...

Step 5.1.1.1

Cancel the common factor of $30$ .

Tap for more steps...

Step 5.1.1.1.1

Move the leading negative in $- \frac{z}{30}$ into the numerator.

$- 30 \frac{- z}{30} = - 30 (- \frac{53}{5})$

Step 5.1.1.1.2

Factor $30$ out of $- 30$ .

$30 (- 1) \frac{- z}{30} = - 30 (- \frac{53}{5})$

Step 5.1.1.1.3

Cancel the common factor.

$30 \cdot - 1 \frac{- z}{30} = - 30 (- \frac{53}{5})$

Step 5.1.1.1.4

Rewrite the expression.

$- - z = - 30 (- \frac{53}{5})$

Step 5.1.1.2

Multiply.

Tap for more steps...

Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 z = - 30 (- \frac{53}{5})$

Step 5.1.1.2.2

Multiply $z$ by $1$ .

$z = - 30 (- \frac{53}{5})$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Simplify $- 30 (- \frac{53}{5})$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor of $5$ .

Tap for more steps...

Step 5.2.1.1.1

Move the leading negative in $- \frac{53}{5}$ into the numerator.

$z = - 30 (\frac{- 53}{5})$

Step 5.2.1.1.2

Factor $5$ out of $- 30$ .

$z = 5 (- 6) \frac{- 53}{5}$

Step 5.2.1.1.3

Cancel the common factor.

$z = 5 \cdot - 6 \frac{- 53}{5}$

Step 5.2.1.1.4

Rewrite the expression.

$z = - 6 \cdot - 53$

Step 5.2.1.2

Multiply $- 6$ by $- 53$ .

$z = 318$