Solve 1-2x+1/5>x+2

$$1- \frac{ 2x+1 }{ 5 } > x+2$$

Solve for x

$$x<-\frac{6}{7}$$

Solution Steps

Multiply both sides of the equation by 5. Since 5 is positive, the inequality direction remains the same.

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

To find the opposite of 2x+1, find the opposite of each term.

$$5-2x-1>5x+10$$

Subtract 1 from 5 to get 4.

$$4-2x>5x+10$$

Subtract 5x from both sides.

$$4-2x-5x>10$$

Combine -2x and -5x to get -7x.

$$4-7x>10$$

Subtract 4 from both sides.

$$-7x>10-4$$

Subtract 4 from 10 to get 6.

$$-7x>6$$

Divide both sides by -7. Since -7 is negative, the inequality direction is changed.

$$x<-\frac{6}{7}$$