Solve 5/2(x-8)+3(3/4x+2)

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

Evaluate

$$\frac{19x}{4}-14$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by x-8.

$$\frac{5}{2}x+\frac{5}{2}\left(-8\right)+3\left(\frac{3}{4}x+2\right)$$

Express \frac{5}{2}\left(-8\right) as a single fraction.

$$\frac{5}{2}x+\frac{5\left(-8\right)}{2}+3\left(\frac{3}{4}x+2\right)$$

Multiply 5 and -8 to get -40.

$$\frac{5}{2}x+\frac{-40}{2}+3\left(\frac{3}{4}x+2\right)$$

Divide -40 by 2 to get -20.

$$\frac{5}{2}x-20+3\left(\frac{3}{4}x+2\right)$$

Use the distributive property to multiply 3 by \frac{3}{4}x+2.

$$\frac{5}{2}x-20+3\times \frac{3}{4}x+6$$

Express 3\times \frac{3}{4} as a single fraction.

$$\frac{5}{2}x-20+\frac{3\times 3}{4}x+6$$

Multiply 3 and 3 to get 9.

$$\frac{5}{2}x-20+\frac{9}{4}x+6$$

Combine \frac{5}{2}x and \frac{9}{4}x to get \frac{19}{4}x.

$$\frac{19}{4}x-20+6$$

Add -20 and 6 to get -14.

$$\frac{19}{4}x-14$$

Expand

$$\frac{19x}{4}-14$$

Solution Steps

Use the distributive property to multiply \frac{5}{2} by x-8.

$$\frac{5}{2}x+\frac{5}{2}\left(-8\right)+3\left(\frac{3}{4}x+2\right)$$

Express \frac{5}{2}\left(-8\right) as a single fraction.

$$\frac{5}{2}x+\frac{5\left(-8\right)}{2}+3\left(\frac{3}{4}x+2\right)$$

Multiply 5 and -8 to get -40.

$$\frac{5}{2}x+\frac{-40}{2}+3\left(\frac{3}{4}x+2\right)$$

Divide -40 by 2 to get -20.

$$\frac{5}{2}x-20+3\left(\frac{3}{4}x+2\right)$$

Use the distributive property to multiply 3 by \frac{3}{4}x+2.

$$\frac{5}{2}x-20+3\times \frac{3}{4}x+6$$

Express 3\times \frac{3}{4} as a single fraction.

$$\frac{5}{2}x-20+\frac{3\times 3}{4}x+6$$

Multiply 3 and 3 to get 9.

$$\frac{5}{2}x-20+\frac{9}{4}x+6$$

Combine \frac{5}{2}x and \frac{9}{4}x to get \frac{19}{4}x.

$$\frac{19}{4}x-20+6$$

Add -20 and 6 to get -14.

$$\frac{19}{4}x-14$$