Simplify 3/4(3x+6)-1/4(5x-24)

$\frac{3}{4} (3 x + 6) - \frac{1}{4} (5 x - 24)$

Step 1

Simplify each term.

Apply the distributive property.

$\frac{3}{4} (3 x) + \frac{3}{4} \cdot 6 - \frac{1}{4} \cdot (5 x - 24)$

Multiply $\frac{3}{4} (3 x)$ .

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

$\frac{3 \cdot 3}{4} x + \frac{3}{4} \cdot 6 - \frac{1}{4} \cdot (5 x - 24)$

Multiply $3$ by $3$ .

$\frac{9}{4} x + \frac{3}{4} \cdot 6 - \frac{1}{4} \cdot (5 x - 24)$

Combine $\frac{9}{4}$ and $x$ .

$\frac{9 x}{4} + \frac{3}{4} \cdot 6 - \frac{1}{4} \cdot (5 x - 24)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{9 x}{4} + \frac{3}{2 (2)} \cdot 6 - \frac{1}{4} \cdot (5 x - 24)$

Factor $2$ out of $6$ .

$\frac{9 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot 3) - \frac{1}{4} \cdot (5 x - 24)$

Cancel the common factor.

$\frac{9 x}{4} + \frac{3}{2 \cdot 2} \cdot (2 \cdot 3) - \frac{1}{4} \cdot (5 x - 24)$

Rewrite the expression.

$\frac{9 x}{4} + \frac{3}{2} \cdot 3 - \frac{1}{4} \cdot (5 x - 24)$

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

$\frac{9 x}{4} + \frac{3 \cdot 3}{2} - \frac{1}{4} \cdot (5 x - 24)$

Multiply $3$ by $3$ .

$\frac{9 x}{4} + \frac{9}{2} - \frac{1}{4} \cdot (5 x - 24)$

Apply the distributive property.

$\frac{9 x}{4} + \frac{9}{2} - \frac{1}{4} (5 x) - \frac{1}{4} \cdot - 24$

Multiply $- \frac{1}{4} (5 x)$ .

Multiply $5$ by $- 1$ .

$\frac{9 x}{4} + \frac{9}{2} - 5 (\frac{1}{4}) x - \frac{1}{4} \cdot - 24$

Combine $- 5$ and $\frac{1}{4}$ .

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5}{4} x - \frac{1}{4} \cdot - 24$

Combine $\frac{- 5}{4}$ and $x$ .

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} - \frac{1}{4} \cdot - 24$

Cancel the common factor of $4$ .

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

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} + \frac{- 1}{4} \cdot - 24$

Factor $4$ out of $- 24$ .

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} + \frac{- 1}{4} \cdot (4 (- 6))$

Cancel the common factor.

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} + \frac{- 1}{4} \cdot (4 \cdot - 6)$

Rewrite the expression.

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} - 1 \cdot - 6$

Multiply $- 1$ by $- 6$ .

$\frac{9 x}{4} + \frac{9}{2} + \frac{- 5 x}{4} + 6$

Move the negative in front of the fraction.

$\frac{9 x}{4} + \frac{9}{2} - \frac{5 x}{4} + 6$

Step 2

Simplify terms.

Combine the numerators over the common denominator.

$6 + \frac{9 x - 5 x}{4} + \frac{9}{2}$

Subtract $5 x$ from $9 x$ .

$6 + \frac{4 x}{4} + \frac{9}{2}$

Cancel the common factor of $4$ .

Cancel the common factor.

$6 + \frac{4 x}{4} + \frac{9}{2}$

Divide $x$ by $1$ .

$6 + x + \frac{9}{2}$

Step 3

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x + 6 \cdot \frac{2}{2} + \frac{9}{2}$

Step 4

Combine $6$ and $\frac{2}{2}$ .

$x + \frac{6 \cdot 2}{2} + \frac{9}{2}$

Step 5

Combine the numerators over the common denominator.

$x + \frac{6 \cdot 2 + 9}{2}$

Step 6

Simplify the numerator.

Multiply $6$ by $2$ .

$x + \frac{12 + 9}{2}$

Add $12$ and $9$ .

$x + \frac{21}{2}$

Simplify 3/4(3x+6)-1/4(5x-24)

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