Solve -5+2x<1/2x-7

$$- 5 + 2 x < \frac { 1 } { 2 } x - 7$$

Solve for x

$$x<-\frac{4}{3}$$

Solution Steps

Subtract \frac{1}{2}x from both sides.

$$-5+2x-\frac{1}{2}x<-7$$

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

$$-5+\frac{3}{2}x<-7$$

Add 5 to both sides.

$$\frac{3}{2}x<-7+5$$

Add -7 and 5 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.

$$x<\frac{-4}{3}$$

Fraction \frac{-4}{3} can be rewritten as -\frac{4}{3} by extracting the negative sign.

$$x<-\frac{4}{3}$$