Solve 9x-(x-77)>x+21

$$9 x - ( x - 77 ) > x + 21$$

Solve for x

$$x>-8$$

Solution Steps

To find the opposite of x-77, find the opposite of each term.

$$9x-x-\left(-77\right)>x+21$$

The opposite of -77 is 77.

$$9x-x+77>x+21$$

Combine 9x and -x to get 8x.

$$8x+77>x+21$$

Subtract x from both sides.

$$8x+77-x>21$$

Combine 8x and -x to get 7x.

$$7x+77>21$$

Subtract 77 from both sides.

$$7x>21-77$$

Subtract 77 from 21 to get -56.

$$7x>-56$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x>\frac{-56}{7}$$

Divide -56 by 7 to get -8.

$$x>-8$$