Solve 5-2(x+1)<2(x+5)+13

$$5-2(x+1) < 2(x+5)+13$$

Solve for x

$$x>-5$$

Solution Steps

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

$$5-2x-2<2\left(x+5\right)+13$$

Subtract 2 from 5 to get 3.

$$3-2x<2\left(x+5\right)+13$$

Use the distributive property to multiply 2 by x+5.

$$3-2x<2x+10+13$$

Add 10 and 13 to get 23.

$$3-2x<2x+23$$

Subtract 2x from both sides.

$$3-2x-2x<23$$

Combine -2x and -2x to get -4x.

$$3-4x<23$$

Subtract 3 from both sides.

$$-4x<23-3$$

Subtract 3 from 23 to get 20.

$$-4x<20$$

Divide both sides by -4. Since -4 is negative, the inequality direction is changed.

$$x>\frac{20}{-4}$$

Divide 20 by -4 to get -5.

$$x>-5$$