Solve 3/2x+2>2(8-x)

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

Solve for x

$$x>4$$

Solution Steps

Use the distributive property to multiply 2 by 8-x.

$$\frac{3}{2}x+2>16-2x$$

Add 2x to both sides.

$$\frac{3}{2}x+2+2x>16$$

Combine \frac{3}{2}x and 2x to get \frac{7}{2}x.

$$\frac{7}{2}x+2>16$$

Subtract 2 from both sides.

$$\frac{7}{2}x>16-2$$

Subtract 2 from 16 to get 14.

$$\frac{7}{2}x>14$$

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}. Since \frac{7}{2} is positive, the inequality direction remains the same.

$$x>14\times \frac{2}{7}$$

Express 14\times \frac{2}{7} as a single fraction.

$$x>\frac{14\times 2}{7}$$

Multiply 14 and 2 to get 28.

$$x>\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$x>4$$