Solve 1/2x+1>2/3x-3

$$\frac { 1 } { 2 } x + 1 > \frac { 2 } { 3 } x - 3$$

Solve for x

$$x<24$$

Solution Steps

Subtract \frac{2}{3}x from both sides.

$$\frac{1}{2}x+1-\frac{2}{3}x>-3$$

Combine \frac{1}{2}x and -\frac{2}{3}x to get -\frac{1}{6}x.

$$-\frac{1}{6}x+1>-3$$

Subtract 1 from both sides.

$$-\frac{1}{6}x>-3-1$$

Subtract 1 from -3 to get -4.

$$-\frac{1}{6}x>-4$$

Multiply both sides by -6, the reciprocal of -\frac{1}{6}. Since -\frac{1}{6} is negative, the inequality direction is changed.

$$x<-4\left(-6\right)$$

Multiply -4 and -6 to get 24.

$$x<24$$