Solve 2(x+1)-5<3(x-1)+4

$$2 ( x + 1 ) - 5 < 3 ( x - 1 ) + 4$$

Solve for x

$$x>-4$$

Solution Steps

Use the distributive property to multiply 2 by x+1.

$$2x+2-5<3\left(x-1\right)+4$$

Subtract 5 from 2 to get -3.

$$2x-3<3\left(x-1\right)+4$$

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

$$2x-3<3x-3+4$$

Add -3 and 4 to get 1.

$$2x-3<3x+1$$

Subtract 3x from both sides.

$$2x-3-3x<1$$

Combine 2x and -3x to get -x.

$$-x-3<1$$

Add 3 to both sides.

$$-x<1+3$$

Add 1 and 3 to get 4.

$$-x<4$$

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

$$x>-4$$