Solve 12x-3x+11>4x-(17-9x)

$$12 x - 3 x + 11 > 4 x - ( 17 - 9 x )$$

Solve for x

$$x<7$$

Solution Steps

Combine 12x and -3x to get 9x.

$$9x+11>4x-\left(17-9x\right)$$

To find the opposite of 17-9x, find the opposite of each term.

$$9x+11>4x-17-\left(-9x\right)$$

The opposite of -9x is 9x.

$$9x+11>4x-17+9x$$

Combine 4x and 9x to get 13x.

$$9x+11>13x-17$$

Subtract 13x from both sides.

$$9x+11-13x>-17$$

Combine 9x and -13x to get -4x.

$$-4x+11>-17$$

Subtract 11 from both sides.

$$-4x>-17-11$$

Subtract 11 from -17 to get -28.

$$-4x>-28$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x<\frac{-28}{-4}$$

Divide -28 by -4 to get 7.

$$x<7$$