Question

How do I Solve and graph the inequality |6 – v| < 9?

a. Write the inequality as two inequalities without absolute value.
b. Solve the inequality and write the solution set.
and
c. Graph the solution on a number line?

Answer 1

|6 – v| < 9 can be written as two separate inequalities:

+(6 - v) < 9, or -v < 3, or v > -3: (-3, infinity)

-(6-v) < 9, or -6 + v < 9, or v<15: (-infinity, 15)

These two intervals overlap: (-3,15)