Algebra Examples

$(- \frac{7}{2} z + 4) + (\frac{1}{5} z - 15)$

Step 1

Remove parentheses.

$- \frac{7}{2} z + 4 + \frac{1}{5} z - 15$

Step 2

Simplify each term.

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Step 2.1

Combine $z$ and $\frac{7}{2}$ .

$- \frac{z \cdot 7}{2} + 4 + \frac{1}{5} z - 15$

Step 2.2

Move $7$ to the left of $z$ .

$- \frac{7 \cdot z}{2} + 4 + \frac{1}{5} z - 15$

Step 2.3

Combine $\frac{1}{5}$ and $z$ .

$- \frac{7 z}{2} + 4 + \frac{z}{5} - 15$

Step 3

To write $- \frac{7 z}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7 z}{2} \cdot \frac{5}{5} + \frac{z}{5} + 4 - 15$

Step 4

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

$- \frac{7 z}{2} \cdot \frac{5}{5} + \frac{z}{5} \cdot \frac{2}{2} + 4 - 15$

Step 5

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{7 z}{2}$ by $\frac{5}{5}$ .

$- \frac{7 z \cdot 5}{2 \cdot 5} + \frac{z}{5} \cdot \frac{2}{2} + 4 - 15$

Step 5.2

Multiply $2$ by $5$ .

$- \frac{7 z \cdot 5}{10} + \frac{z}{5} \cdot \frac{2}{2} + 4 - 15$

Step 5.3

Multiply $\frac{z}{5}$ by $\frac{2}{2}$ .

$- \frac{7 z \cdot 5}{10} + \frac{z \cdot 2}{5 \cdot 2} + 4 - 15$

Step 5.4

Multiply $5$ by $2$ .

$- \frac{7 z \cdot 5}{10} + \frac{z \cdot 2}{10} + 4 - 15$

Step 6

Combine the numerators over the common denominator.

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + 4 - 15$

Step 7

Find the common denominator.

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Step 7.1

Write $4$ as a fraction with denominator $1$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4}{1} - 15$

Step 7.2

Multiply $\frac{4}{1}$ by $\frac{10}{10}$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4}{1} \cdot \frac{10}{10} - 15$

Step 7.3

Multiply $\frac{4}{1}$ by $\frac{10}{10}$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4 \cdot 10}{10} - 15$

Step 7.4

Write $- 15$ as a fraction with denominator $1$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4 \cdot 10}{10} + \frac{- 15}{1}$

Step 7.5

Multiply $\frac{- 15}{1}$ by $\frac{10}{10}$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4 \cdot 10}{10} + \frac{- 15}{1} \cdot \frac{10}{10}$

Step 7.6

Multiply $\frac{- 15}{1}$ by $\frac{10}{10}$ .

$\frac{- 7 z \cdot 5 + z \cdot 2}{10} + \frac{4 \cdot 10}{10} + \frac{- 15 \cdot 10}{10}$

Step 8

Combine the numerators over the common denominator.

$\frac{- 7 z \cdot 5 + z \cdot 2 + 4 \cdot 10 - 15 \cdot 10}{10}$

Step 9

Simplify each term.

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Step 9.1

Multiply $5$ by $- 7$ .

$\frac{- 35 z + z \cdot 2 + 4 \cdot 10 - 15 \cdot 10}{10}$

Step 9.2

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

$\frac{- 35 z + 2 \cdot z + 4 \cdot 10 - 15 \cdot 10}{10}$

Step 9.3

Multiply $4$ by $10$ .

$\frac{- 35 z + 2 z + 40 - 15 \cdot 10}{10}$

Step 9.4

Multiply $- 15$ by $10$ .

$\frac{- 35 z + 2 z + 40 - 150}{10}$

Step 10

Simplify terms.

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Step 10.1

Add $- 35 z$ and $2 z$ .

$\frac{- 33 z + 40 - 150}{10}$

Step 10.2

Subtract $150$ from $40$ .

$\frac{- 33 z - 110}{10}$

Step 10.3

Factor $11$ out of $- 33 z - 110$ .

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Step 10.3.1

Factor $11$ out of $- 33 z$ .

$\frac{11 (- 3 z) - 110}{10}$

Step 10.3.2

Factor $11$ out of $- 110$ .

$\frac{11 (- 3 z) + 11 (- 10)}{10}$

Step 10.3.3

Factor $11$ out of $11 (- 3 z) + 11 (- 10)$ .

$\frac{11 (- 3 z - 10)}{10}$

Step 10.4

Factor $- 1$ out of $- 3 z$ .

$\frac{11 (- (3 z) - 10)}{10}$

Step 10.5

Rewrite $- 10$ as $- 1 (10)$ .

$\frac{11 (- (3 z) - 1 (10))}{10}$

Step 10.6

Factor $- 1$ out of $- (3 z) - 1 (10)$ .

$\frac{11 (- (3 z + 10))}{10}$

Step 10.7

Simplify the expression.

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Step 10.7.1

Rewrite $- (3 z + 10)$ as $- 1 (3 z + 10)$ .

$\frac{11 (- 1 (3 z + 10))}{10}$

Step 10.7.2

Move the negative in front of the fraction.

$- \frac{11 (3 z + 10)}{10}$