Solve 1-x/2<-7x+2/5-1

$$\frac { 1 - x } { 2 } < - \frac { 7 x + 2 } { 5 } - 1$$

Solve for x

$$x<-\frac{19}{9}$$

Solution Steps

Multiply both sides of the equation by 10, the least common multiple of 2,5. Since 10 is positive, the inequality direction remains the same.

$$5\left(1-x\right)<-2\left(7x+2\right)-10$$

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

$$5-5x<-2\left(7x+2\right)-10$$

Use the distributive property to multiply -2 by 7x+2.

$$5-5x<-14x-4-10$$

Subtract 10 from -4 to get -14.

$$5-5x<-14x-14$$

Add 14x to both sides.

$$5-5x+14x<-14$$

Combine -5x and 14x to get 9x.

$$5+9x<-14$$

Subtract 5 from both sides.

$$9x<-14-5$$

Subtract 5 from -14 to get -19.

$$9x<-19$$

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

$$x<-\frac{19}{9}$$