Algebra Examples

$\frac{9}{4} (\frac{10}{3} x - 4) - \frac{1}{4} (2 x - 8)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{10}{3}$ and $x$ .

$\frac{9}{4} \cdot (\frac{10 x}{3} - 4) - \frac{1}{4} \cdot (2 x - 8)$

Step 1.2

Apply the distributive property.

$\frac{9}{4} \cdot \frac{10 x}{3} + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $9$ .

$\frac{3 (3)}{4} \cdot \frac{10 x}{3} + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.3.2

Cancel the common factor.

$\frac{3 \cdot 3}{4} \cdot \frac{10 x}{3} + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.3.3

Rewrite the expression.

$\frac{3}{4} (10 x) + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $4$ .

$\frac{3}{2 (2)} (10 x) + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.4.2

Factor $2$ out of $10 x$ .

$\frac{3}{2 (2)} (2 (5 x)) + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.4.3

Cancel the common factor.

$\frac{3}{2 \cdot 2} (2 (5 x)) + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.4.4

Rewrite the expression.

$\frac{3}{2} (5 x) + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.5

Combine $5$ and $\frac{3}{2}$ .

$\frac{5 \cdot 3}{2} x + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.6

Multiply $5$ by $3$ .

$\frac{15}{2} x + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.7

Combine $\frac{15}{2}$ and $x$ .

$\frac{15 x}{2} + \frac{9}{4} \cdot - 4 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.8

Cancel the common factor of $4$ .

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Step 1.8.1

Factor $4$ out of $- 4$ .

$\frac{15 x}{2} + \frac{9}{4} \cdot (4 (- 1)) - \frac{1}{4} \cdot (2 x - 8)$

Step 1.8.2

Cancel the common factor.

$\frac{15 x}{2} + \frac{9}{4} \cdot (4 \cdot - 1) - \frac{1}{4} \cdot (2 x - 8)$

Step 1.8.3

Rewrite the expression.

$\frac{15 x}{2} + 9 \cdot - 1 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.9

Multiply $9$ by $- 1$ .

$\frac{15 x}{2} - 9 - \frac{1}{4} \cdot (2 x - 8)$

Step 1.10

Apply the distributive property.

$\frac{15 x}{2} - 9 - \frac{1}{4} (2 x) - \frac{1}{4} \cdot - 8$

Step 1.11

Cancel the common factor of $2$ .

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Step 1.11.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{15 x}{2} - 9 + \frac{- 1}{4} (2 x) - \frac{1}{4} \cdot - 8$

Step 1.11.2

Factor $2$ out of $4$ .

$\frac{15 x}{2} - 9 + \frac{- 1}{2 (2)} (2 x) - \frac{1}{4} \cdot - 8$

Step 1.11.3

Factor $2$ out of $2 x$ .

$\frac{15 x}{2} - 9 + \frac{- 1}{2 (2)} (2 (x)) - \frac{1}{4} \cdot - 8$

Step 1.11.4

Cancel the common factor.

$\frac{15 x}{2} - 9 + \frac{- 1}{2 \cdot 2} (2 x) - \frac{1}{4} \cdot - 8$

Step 1.11.5

Rewrite the expression.

$\frac{15 x}{2} - 9 + \frac{- 1}{2} x - \frac{1}{4} \cdot - 8$

Step 1.12

Combine $\frac{- 1}{2}$ and $x$ .

$\frac{15 x}{2} - 9 + \frac{- x}{2} - \frac{1}{4} \cdot - 8$

Step 1.13

Cancel the common factor of $4$ .

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Step 1.13.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{15 x}{2} - 9 + \frac{- x}{2} + \frac{- 1}{4} \cdot - 8$

Step 1.13.2

Factor $4$ out of $- 8$ .

$\frac{15 x}{2} - 9 + \frac{- x}{2} + \frac{- 1}{4} \cdot (4 (- 2))$

Step 1.13.3

Cancel the common factor.

$\frac{15 x}{2} - 9 + \frac{- x}{2} + \frac{- 1}{4} \cdot (4 \cdot - 2)$

Step 1.13.4

Rewrite the expression.

$\frac{15 x}{2} - 9 + \frac{- x}{2} - 1 \cdot - 2$

Step 1.14

Multiply $- 1$ by $- 2$ .

$\frac{15 x}{2} - 9 + \frac{- x}{2} + 2$

Step 1.15

Move the negative in front of the fraction.

$\frac{15 x}{2} - 9 - \frac{x}{2} + 2$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$- 9 + 2 + \frac{15 x - x}{2}$

Step 2.2

Subtract $x$ from $15 x$ .

$- 9 + 2 + \frac{14 x}{2}$

Step 2.3

Cancel the common factor of $14$ and $2$ .

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Step 2.3.1

Factor $2$ out of $14 x$ .

$- 9 + 2 + \frac{2 (7 x)}{2}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $2$ .

$- 9 + 2 + \frac{2 (7 x)}{2 (1)}$

Step 2.3.2.2

Cancel the common factor.

$- 9 + 2 + \frac{2 (7 x)}{2 \cdot 1}$

Step 2.3.2.3

Rewrite the expression.

$- 9 + 2 + \frac{7 x}{1}$

Step 2.3.2.4

Divide $7 x$ by $1$ .

$- 9 + 2 + 7 x$

Step 2.4

Add $- 9$ and $2$ .

$- 7 + 7 x$