Solve x+3(x-5)<7-[x+4-2(3x+2)]

$$x + 3 ( x - 5 ) < 7 - [ x + 4 - 2 ( 3 x + 2 ) ]$$

Solve for x

$$x>-22$$

Solution Steps

Use the distributive property to multiply 3 by x-5.

$$x+3x-15<7-\left(x+4-2\left(3x+2\right)\right)$$

Combine x and 3x to get 4x.

$$4x-15<7-\left(x+4-2\left(3x+2\right)\right)$$

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

$$4x-15<7-\left(x+4-6x-4\right)$$

Combine x and -6x to get -5x.

$$4x-15<7-\left(-5x+4-4\right)$$

Subtract 4 from 4 to get 0.

$$4x-15<7-\left(-5x\right)$$

The opposite of -5x is 5x.

$$4x-15<7+5x$$

Subtract 5x from both sides.

$$4x-15-5x<7$$

Combine 4x and -5x to get -x.

$$-x-15<7$$

Add 15 to both sides.

$$-x<7+15$$

Add 7 and 15 to get 22.

$$-x<22$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>-22$$