Solve 3/4x+2<5/8x-3

$$\frac { 3 } { 4 } x + 2 < \frac { 5 } { 8 } x - 3$$

Solve for x

$$x<-40$$

Solution Steps

Subtract \frac{5}{8}x from both sides.

$$\frac{3}{4}x+2-\frac{5}{8}x<-3$$

Combine \frac{3}{4}x and -\frac{5}{8}x to get \frac{1}{8}x.

$$\frac{1}{8}x+2<-3$$

Subtract 2 from both sides.

$$\frac{1}{8}x<-3-2$$

Subtract 2 from -3 to get -5.

$$\frac{1}{8}x<-5$$

Multiply both sides by 8, the reciprocal of \frac{1}{8}. Since \frac{1}{8} is positive, the inequality direction remains the same.

$$x<-5\times 8$$

Multiply -5 and 8 to get -40.

$$x<-40$$