Solve 5/2x+4>x+6

$$\frac { 5 } { 2 } x + 4 > x + 6$$

Solve for x

$$x>\frac{4}{3}$$

Solution Steps

Subtract x from both sides.

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

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

$$\frac{3}{2}x+4>6$$

Subtract 4 from both sides.

$$\frac{3}{2}x>6-4$$

Subtract 4 from 6 to get 2.

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

Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}. Since \frac{3}{2} is positive, the inequality direction remains the same.

$$x>2\times \frac{2}{3}$$

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

$$x>\frac{2\times 2}{3}$$

Multiply 2 and 2 to get 4.

$$x>\frac{4}{3}$$