Solve 3(x+1)-2(x+2)>2(x-3)

$$3 ( x + 1 ) - 2 ( x + 2 ) > 2 ( x - 3 )$$

Solve for x

$$x<5$$

Solution Steps

Use the distributive property to multiply 3 by x+1.

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

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

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

Combine 3x and -2x to get x.

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

Subtract 4 from 3 to get -1.

$$x-1>2\left(x-3\right)$$

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

$$x-1>2x-6$$

Subtract 2x from both sides.

$$x-1-2x>-6$$

Combine x and -2x to get -x.

$$-x-1>-6$$

Add 1 to both sides.

$$-x>-6+1$$

Add -6 and 1 to get -5.

$$-x>-5$$

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

$$x<\frac{-5}{-1}$$

Fraction \frac{-5}{-1} can be simplified to 5 by removing the negative sign from both the numerator and the denominator.

$$x<5$$