Absolute Value

Question

l 5x+3l -7 < 1

 

a. x< 3/5 or > 11/5

 

b. 3/5 < x < 11/5

 

c. x < -11/5 or x >1

 

d. -11/5 < x <1

Answer 1

Rewrite the inequality as follows:

|5x + 3| < 8

Make the two cases for absolute value inequalities as follows:

1) 5x + 3 < 8
2) 5x + 3 > -8

Now, solve both cases.
1) 5x + 3 < 8
or 5x < 5
or x < 1

2) 5x + 3 > -8

or 5x > -11
or x > -11/5

Combine the solution of both cases to get
-11/5 < x < 1

That is answer choice d.