Solve the inequality: -4| 5x+12| -13> -44

-79/20 < x< -17/20

Step-by-step explanation:

-4| 5x+12| -13> -44

The first step is to add 13 to each side

-4| 5x+12| -13+13> -44+13

-4| 5x+12| > -31

Divide each side by -4.  Remember when dividing by a negative to flip the inequality

-4/-4| 5x+12| < -31/-4

| 5x+12| < 31/4

Now we will have 2 equations, one positive and one negative.  Remember to flip the inequality for the negative

5x+12 < 31/4   and 5x+12 >-31/4

Subtract 12 from each side

5x+12-12 < 31/4-12   and 5x+12-12 >-31/4-12

5x < 31/4-12   and 5x >-31/4-12

Get a common denominator of 4

5x < 31/4-48/4   and 5x >-31/4-48/4

5x < -17/4       and   5x > -79/4

Divide each side by 5

x < -17/20    and x >-79/20

-79/20 < x< -17/20

(a) the volume of the cone is 20/3 in3

hence, option a is correct.