Home > Algebra > Absolute Value Inequalities

How do you solve #abs(7x+5)<23#?

Answer 1

Ethan Adkins

#x in (-4, 18/7)#

By the property: #|a| < b ==> -b < a < b# #-23 < 7x + 5 < 23#

#-23 - 5 < 7x < 23 - 5#

#-28/7 < x < 18/7#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

To solve the inequality |7x + 5| < 23, you first isolate the absolute value expression by considering two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (7x + 5) is positive: 7x + 5 < 23

Case 2: (7x + 5) is negative: -(7x + 5) < 23

Solve each case separately to find the possible values of x. Then, combine the solutions.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #abs(7x+5)&lt;23#?

How do you solve #abs(7x+5)<23#?