Solve 1/2x+3<2x-6

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

Solve for x

$$x>6$$

Solution Steps

Subtract 2x from both sides.

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

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

$$-\frac{3}{2}x+3<-6$$

Subtract 3 from both sides.

$$-\frac{3}{2}x<-6-3$$

Subtract 3 from -6 to get -9.

$$-\frac{3}{2}x<-9$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.

$$x>-9\left(-\frac{2}{3}\right)$$

Express -9\left(-\frac{2}{3}\right) as a single fraction.

$$x>\frac{-9\left(-2\right)}{3}$$

Multiply -9 and -2 to get 18.

$$x>\frac{18}{3}$$

Divide 18 by 3 to get 6.

$$x>6$$