Algebra Examples

$(\frac{3}{4} x - 27) - (7 x - 35)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} - 27 - (7 x - 35)$

Step 1.2

Apply the distributive property.

$\frac{3 x}{4} - 27 - (7 x) - - 35$

Step 1.3

Multiply $7$ by $- 1$ .

$\frac{3 x}{4} - 27 - 7 x - - 35$

Step 1.4

Multiply $- 1$ by $- 35$ .

$\frac{3 x}{4} - 27 - 7 x + 35$

Step 2

To write $- 7 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} - 7 x \cdot \frac{4}{4} - 27 + 35$

Step 3

Combine $- 7 x$ and $\frac{4}{4}$ .

$\frac{3 x}{4} + \frac{- 7 x \cdot 4}{4} - 27 + 35$

Step 4

Combine the numerators over the common denominator.

$\frac{3 x - 7 x \cdot 4}{4} - 27 + 35$

Step 5

Find the common denominator.

Tap for more steps...

Step 5.1

Write $- 27$ as a fraction with denominator $1$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27}{1} + 35$

Step 5.2

Multiply $\frac{- 27}{1}$ by $\frac{4}{4}$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27}{1} \cdot \frac{4}{4} + 35$

Step 5.3

Multiply $\frac{- 27}{1}$ by $\frac{4}{4}$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27 \cdot 4}{4} + 35$

Step 5.4

Write $35$ as a fraction with denominator $1$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27 \cdot 4}{4} + \frac{35}{1}$

Step 5.5

Multiply $\frac{35}{1}$ by $\frac{4}{4}$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27 \cdot 4}{4} + \frac{35}{1} \cdot \frac{4}{4}$

Step 5.6

Multiply $\frac{35}{1}$ by $\frac{4}{4}$ .

$\frac{3 x - 7 x \cdot 4}{4} + \frac{- 27 \cdot 4}{4} + \frac{35 \cdot 4}{4}$

Step 6

Combine the numerators over the common denominator.

$\frac{3 x - 7 x \cdot 4 - 27 \cdot 4 + 35 \cdot 4}{4}$

Step 7

Simplify each term.

Tap for more steps...

Step 7.1

Multiply $4$ by $- 7$ .

$\frac{3 x - 28 x - 27 \cdot 4 + 35 \cdot 4}{4}$

Step 7.2

Multiply $- 27$ by $4$ .

$\frac{3 x - 28 x - 108 + 35 \cdot 4}{4}$

Step 7.3

Multiply $35$ by $4$ .

$\frac{3 x - 28 x - 108 + 140}{4}$

Step 8

Simplify terms.

Tap for more steps...

Step 8.1

Subtract $28 x$ from $3 x$ .

$\frac{- 25 x - 108 + 140}{4}$

Step 8.2

Add $- 108$ and $140$ .

$\frac{- 25 x + 32}{4}$

Step 8.3

Factor $- 1$ out of $- 25 x$ .

$\frac{- (25 x) + 32}{4}$

Step 8.4

Rewrite $32$ as $- 1 (- 32)$ .

$\frac{- (25 x) - 1 (- 32)}{4}$

Step 8.5

Factor $- 1$ out of $- (25 x) - 1 (- 32)$ .

$\frac{- (25 x - 32)}{4}$

Step 8.6

Simplify the expression.

Tap for more steps...

Step 8.6.1

Rewrite $- (25 x - 32)$ as $- 1 (25 x - 32)$ .

$\frac{- 1 (25 x - 32)}{4}$

Step 8.6.2

Move the negative in front of the fraction.

$- \frac{25 x - 32}{4}$