Solve 2x-8x+15<7x+2x-8+2

$$2 x - 8 x + 15 < 7 x + 2 x - 8 + 2$$

Solve for x

$$x>\frac{7}{5}$$

Solution Steps

Combine 2x and -8x to get -6x.

$$-6x+15<7x+2x-8+2$$

Combine 7x and 2x to get 9x.

$$-6x+15<9x-8+2$$

Add -8 and 2 to get -6.

$$-6x+15<9x-6$$

Subtract 9x from both sides.

$$-6x+15-9x<-6$$

Combine -6x and -9x to get -15x.

$$-15x+15<-6$$

Subtract 15 from both sides.

$$-15x<-6-15$$

Subtract 15 from -6 to get -21.

$$-15x<-21$$

Divide both sides by -15. Since -15 is negative, the inequality direction is changed.

$$x>\frac{-21}{-15}$$

Reduce the fraction \frac{-21}{-15} to lowest terms by extracting and canceling out -3.

$$x>\frac{7}{5}$$