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

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

Solve for x

$$x<-15$$

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.

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

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

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

The opposite of -5x is 5x.

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

Subtract 1 from 8 to get 7.

$$4\left(-x\right)+7+5x<-8$$

Subtract 7 from both sides.

$$4\left(-x\right)+5x<-8-7$$

Subtract 7 from -8 to get -15.

$$4\left(-x\right)+5x<-15$$

Multiply 4 and -1 to get -4.

$$-4x+5x<-15$$

Combine -4x and 5x to get x.

$$x<-15$$