How do you solve the inequality #abs(2x-3)=5#?

Question

How do you solve the inequality #abs(2x-3)>=5#?

Genesis Allen · Accepted Answer

See a solution process below:

The absolute value function takes any negative or positive term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. #-5 >= 2x - 3 >= 5# First, add #color(red)(3)# to each segment of the system of inequalities to isolate the #x# term while keeping the system balanced: #-5 + color(red)(3) >= 2x - 3 + color(red)(3) >= 5 + color(red)(3)# #-2 >= 2x - 0 >= 8# #-2 >= 2x >= 8# Now, divide each segment by #color(red)(2)# to solve for #x# while keeping the system balanced: #-2/color(red)(2) >= (2x)/color(red)(2) >= 8/color(red)(2)# #-1 >= (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) >= 4# #-1 >= x >= 4# Or #x <= -1#; #x >= 4# Or, in interval notation: #(-oo, -1]; [4, +oo)#

Ethan Adkins · Answer

undefined To solve the inequality |2x - 3| ≥ 5, we consider two cases:

Case 1: 2x - 3 ≥ 5
Solve for x:
2x ≥ 5 + 3
2x ≥ 8
x ≥ 4

Case 2: 2x - 3 ≤ -5
Solve for x:
2x ≤ -5 + 3
2x ≤ -2
x ≤ -1

So, the solution set for the inequality |2x - 3| ≥ 5 is x ≤ -1 or x ≥ 4.

How do you solve the inequality #abs(2x-3)&gt;=5#?

How do you solve the inequality #abs(2x-3)>=5#?