Solve 4(x+2)-5(x+3)<8x+6

$$4 ( x + 2 ) - 5 ( x + 3 ) < 8 x + 6$$

Solve for x

$$x>-\frac{13}{9}$$

Solution Steps

Use the distributive property to multiply 4 by x+2.

$$4x+8-5\left(x+3\right)<8x+6$$

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

$$4x+8-5x-15<8x+6$$

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

$$-x+8-15<8x+6$$

Subtract 15 from 8 to get -7.

$$-x-7<8x+6$$

Subtract 8x from both sides.

$$-x-7-8x<6$$

Combine -x and -8x to get -9x.

$$-9x-7<6$$

Add 7 to both sides.

$$-9x<6+7$$

Add 6 and 7 to get 13.

$$-9x<13$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x>-\frac{13}{9}$$