Solve 9(3x+5)-14(x+2)>3x-2(x+5)

$$9 ( 3 x + 5 ) - 14 ( x + 2 ) > 3 x - 2 ( x + 5 )$$

Solve for x

$$x>-\frac{9}{4}$$

Solution Steps

Use the distributive property to multiply 9 by 3x+5.

$$27x+45-14\left(x+2\right)>3x-2\left(x+5\right)$$

Use the distributive property to multiply -14 by x+2.

$$27x+45-14x-28>3x-2\left(x+5\right)$$

Combine 27x and -14x to get 13x.

$$13x+45-28>3x-2\left(x+5\right)$$

Subtract 28 from 45 to get 17.

$$13x+17>3x-2\left(x+5\right)$$

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

$$13x+17>3x-2x-10$$

Combine 3x and -2x to get x.

$$13x+17>x-10$$

Subtract x from both sides.

$$13x+17-x>-10$$

Combine 13x and -x to get 12x.

$$12x+17>-10$$

Subtract 17 from both sides.

$$12x>-10-17$$

Subtract 17 from -10 to get -27.

$$12x>-27$$

Divide both sides by 12. Since 12 is positive, the inequality direction remains the same.

$$x>\frac{-27}{12}$$

Reduce the fraction \frac{-27}{12} to lowest terms by extracting and canceling out 3.

$$x>-\frac{9}{4}$$