One-Step Absolute Value Equations
What is the solution for lx-4l=x+2
x=1
The temperature in a lab must stay within 3 degrees of 72°F to protect sensitive materials. Write and solve an absolute value inequality that models acceptable temperatures t.
|t-72|≤ 3
69≤ t≤ 75
What is the solution for lx+2l=2x-1
x=3
A company produces phone cases that must weigh exactly 50 grams, with a tolerance of 2.5 grams. Any case outside this range must be rejected.
Write an absolute value inequality and solve for the acceptable weights w.
|w-50|≤ 2.5
47.5≤ w≤ 52.5
What is the solution for ∣3x−2∣=x+4
x=10/3
You are allowed to drive at most 8 mph over or under the speed limit of 55 mph before getting a ticket. Write an absolute value inequality and solve for the speeds s that won’t result in a ticket.
|s-5|≤ 8
47≤ s≤ 63
What is the solution for l3x+2l=4x+5
x=-1
A student’s quiz score differed from the class average of 85 by at most 6 points. Write and solve an absolute value inequality to find the possible scores s the student could have earned.
|s-85|≤ 6
79≤ s≤ 91
3lx/7l>21
x>49,x<-49
What is the solution for l2x+5l=3x+4
x=1
A submarine operates at an ideal depth of –300 meters with a tolerance of 15 meters. Write and solve an inequality to show acceptable depths d.
|d+300|≤15 or |d-(-300)|≤15
-315≤ d≤-285