how to solve absolute value of -8v + 7 <9

Question

How to solve using the absolute value of -8v +7<9.

Answer 1

The inequality is | -8v+7 | < 9.

The absolute value inequality | -8v+7 | < 9 is equivalent to -9 < -8v+7 < 9.

Solve the inequality -9 < -8v+7 < 9.

Subtract 7 from each part.

-9 -7 < -8v+7-7< 9 -7

-16 < -8v < 2

Divide each part by negative 8 and reverse the inequality symbol.

-16/-8 > -8v/-8 > 2/-8

2 > v > -1/4

The solution set is {v | -1/4 < v < 2 }.