Solve 29-2x/3+7<3x-11-x

$$\frac { 29 - 2 x } { 3 } + 7 < 3 x - 11 - x$$

Solve for x

$$x>\frac{83}{8}$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$29-2x+21<9x-33-3x$$

Add 29 and 21 to get 50.

$$50-2x<9x-33-3x$$

Combine 9x and -3x to get 6x.

$$50-2x<6x-33$$

Subtract 6x from both sides.

$$50-2x-6x<-33$$

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

$$50-8x<-33$$

Subtract 50 from both sides.

$$-8x<-33-50$$

Subtract 50 from -33 to get -83.

$$-8x<-83$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$x>\frac{-83}{-8}$$

Fraction \frac{-83}{-8} can be simplified to \frac{83}{8} by removing the negative sign from both the numerator and the denominator.

$$x>\frac{83}{8}$$