Solve 3/2(x+5)-1/4(x+24)

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

Evaluate

$$\frac{5x}{4}+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply \frac{3}{2} by x+5.

$$\frac{3}{2}x+\frac{3}{2}\times 5-\frac{1}{4}\left(x+24\right)$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{3}{2}x+\frac{3\times 5}{2}-\frac{1}{4}\left(x+24\right)$$

Multiply 3 and 5 to get 15.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}\left(x+24\right)$$

Use the distributive property to multiply -\frac{1}{4} by x+24.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x-\frac{1}{4}\times 24$$

Express -\frac{1}{4}\times 24 as a single fraction.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x+\frac{-24}{4}$$

Divide -24 by 4 to get -6.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x-6$$

Combine \frac{3}{2}x and -\frac{1}{4}x to get \frac{5}{4}x.

$$\frac{5}{4}x+\frac{15}{2}-6$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{4}x+\frac{15}{2}-\frac{12}{2}$$

Since \frac{15}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}x+\frac{15-12}{2}$$

Subtract 12 from 15 to get 3.

$$\frac{5}{4}x+\frac{3}{2}$$

Expand

$$\frac{5x}{4}+\frac{3}{2}$$

Solution Steps

Use the distributive property to multiply \frac{3}{2} by x+5.

$$\frac{3}{2}x+\frac{3}{2}\times 5-\frac{1}{4}\left(x+24\right)$$

Express \frac{3}{2}\times 5 as a single fraction.

$$\frac{3}{2}x+\frac{3\times 5}{2}-\frac{1}{4}\left(x+24\right)$$

Multiply 3 and 5 to get 15.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}\left(x+24\right)$$

Use the distributive property to multiply -\frac{1}{4} by x+24.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x-\frac{1}{4}\times 24$$

Express -\frac{1}{4}\times 24 as a single fraction.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x+\frac{-24}{4}$$

Divide -24 by 4 to get -6.

$$\frac{3}{2}x+\frac{15}{2}-\frac{1}{4}x-6$$

Combine \frac{3}{2}x and -\frac{1}{4}x to get \frac{5}{4}x.

$$\frac{5}{4}x+\frac{15}{2}-6$$

Convert 6 to fraction \frac{12}{2}.

$$\frac{5}{4}x+\frac{15}{2}-\frac{12}{2}$$

Since \frac{15}{2} and \frac{12}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{4}x+\frac{15-12}{2}$$

Subtract 12 from 15 to get 3.

$$\frac{5}{4}x+\frac{3}{2}$$