Solve 2/3x+3<-2x-7

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

Solve for x

$$x<-\frac{15}{4}$$

Solution Steps

Add 2x to both sides.

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

Combine \frac{2}{3}x and 2x to get \frac{8}{3}x.

$$\frac{8}{3}x+3<-7$$

Subtract 3 from both sides.

$$\frac{8}{3}x<-7-3$$

Subtract 3 from -7 to get -10.

$$\frac{8}{3}x<-10$$

Multiply both sides by \frac{3}{8}, the reciprocal of \frac{8}{3}. Since \frac{8}{3} is positive, the inequality direction remains the same.

$$x<-10\times \frac{3}{8}$$

Express -10\times \frac{3}{8} as a single fraction.

$$x<\frac{-10\times 3}{8}$$

Multiply -10 and 3 to get -30.

$$x<\frac{-30}{8}$$

Reduce the fraction \frac{-30}{8} to lowest terms by extracting and canceling out 2.

$$x<-\frac{15}{4}$$