Solve 5(x+1)<3/2x-2

$$5 ( x + 1 ) < \frac { 3 } { 2 } x - 2$$

Solve for x

$$x<-2$$

Solution Steps

Use the distributive property to multiply 5 by x+1.

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

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

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

Combine 5x and -\frac{3}{2}x to get \frac{7}{2}x.

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

Subtract 5 from both sides.

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

Subtract 5 from -2 to get -7.

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

Multiply both sides by \frac{2}{7}, the reciprocal of \frac{7}{2}. Since \frac{7}{2} is positive, the inequality direction remains the same.

$$x<-7\times \frac{2}{7}$$

Multiply -7 times \frac{2}{7}.

$$x<-2$$