Solve 7-(x-7)+4(x+2)>7-3(3-2x)

$$7 - ( x - 7 ) + 4 ( x + 2 ) > 7 - 3 ( 3 - 2 x )$$

Solve for x

$$x<8$$

Solution Steps

To find the opposite of x-7, find the opposite of each term.

$$7-x-\left(-7\right)+4\left(x+2\right)>7-3\left(3-2x\right)$$

The opposite of -7 is 7.

$$7-x+7+4\left(x+2\right)>7-3\left(3-2x\right)$$

Add 7 and 7 to get 14.

$$14-x+4\left(x+2\right)>7-3\left(3-2x\right)$$

Use the distributive property to multiply 4 by x+2.

$$14-x+4x+8>7-3\left(3-2x\right)$$

Combine -x and 4x to get 3x.

$$14+3x+8>7-3\left(3-2x\right)$$

Add 14 and 8 to get 22.

$$22+3x>7-3\left(3-2x\right)$$

Use the distributive property to multiply -3 by 3-2x.

$$22+3x>7-9+6x$$

Subtract 9 from 7 to get -2.

$$22+3x>-2+6x$$

Subtract 6x from both sides.

$$22+3x-6x>-2$$

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

$$22-3x>-2$$

Subtract 22 from both sides.

$$-3x>-2-22$$

Subtract 22 from -2 to get -24.

$$-3x>-24$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$x<\frac{-24}{-3}$$

Divide -24 by -3 to get 8.

$$x<8$$