Solve x+2/2-1-5x/8<-1

$$\frac { x + 2 } { 2 } - \frac { 1 - 5 x } { 8 } < - 1$$

Solve for x

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

Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 2,8. Since 8 is positive, the inequality direction remains the same.

$$4\left(x+2\right)-\left(1-5x\right)<-8$$

Use the distributive property to multiply 4 by x+2.

$$4x+8-\left(1-5x\right)<-8$$

To find the opposite of 1-5x, find the opposite of each term.

$$4x+8-1-\left(-5x\right)<-8$$

The opposite of -5x is 5x.

$$4x+8-1+5x<-8$$

Subtract 1 from 8 to get 7.

$$4x+7+5x<-8$$

Combine 4x and 5x to get 9x.

$$9x+7<-8$$

Subtract 7 from both sides.

$$9x<-8-7$$

Subtract 7 from -8 to get -15.

$$9x<-15$$

Divide both sides by 9. Since 9 is positive, the inequality direction remains the same.

$$x<\frac{-15}{9}$$

Reduce the fraction \frac{-15}{9} to lowest terms by extracting and canceling out 3.

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