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

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

Solve for x

$$x>-2$$

Solution Steps

To find the opposite of 5-3x, find the opposite of each term.

$$2x-5-\left(-3x\right)<3\left(3\left(x+3\right)-2\left(2-x\right)\right)$$

The opposite of -3x is 3x.

$$2x-5+3x<3\left(3\left(x+3\right)-2\left(2-x\right)\right)$$

Combine 2x and 3x to get 5x.

$$5x-5<3\left(3\left(x+3\right)-2\left(2-x\right)\right)$$

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

$$5x-5<3\left(3x+9-2\left(2-x\right)\right)$$

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

$$5x-5<3\left(3x+9-4+2x\right)$$

Subtract 4 from 9 to get 5.

$$5x-5<3\left(3x+5+2x\right)$$

Combine 3x and 2x to get 5x.

$$5x-5<3\left(5x+5\right)$$

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

$$5x-5<15x+15$$

Subtract 15x from both sides.

$$5x-5-15x<15$$

Combine 5x and -15x to get -10x.

$$-10x-5<15$$

Add 5 to both sides.

$$-10x<15+5$$

Add 15 and 5 to get 20.

$$-10x<20$$

Divide both sides by -10. Since -10 is negative, the inequality direction is changed.

$$x>\frac{20}{-10}$$

Divide 20 by -10 to get -2.

$$x>-2$$