Solve 2x-9(-13-x)<6x+97+3x

$$2 x - 9 ( - 13 - x ) < 6 x + 97 + 3 x$$

Solve for x

$$x<-10$$

Solution Steps

Use the distributive property to multiply -9 by -13-x.

$$2x+117+9x<6x+97+3x$$

Combine 2x and 9x to get 11x.

$$11x+117<6x+97+3x$$

Combine 6x and 3x to get 9x.

$$11x+117<9x+97$$

Subtract 9x from both sides.

$$11x+117-9x<97$$

Combine 11x and -9x to get 2x.

$$2x+117<97$$

Subtract 117 from both sides.

$$2x<97-117$$

Subtract 117 from 97 to get -20.

$$2x<-20$$

Divide both sides by 2. Since 2 is positive, the inequality direction remains the same.

$$x<\frac{-20}{2}$$

Divide -20 by 2 to get -10.

$$x<-10$$