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Ivan
3 years ago
7

Help Me Please. Which graph represents the solutions to the inequality |2x − 8| < 2?

Mathematics
2 answers:
Lady bird [3.3K]3 years ago
6 0

Given |2x − 8| < 2, simplify this by dividing all terms by 2:


|x − 4| < 1


Think of 4 as the "center." Then the distance from 4 in either direction cannot equal 1 or more. Thus, the third answer choice is the one you want.  The "solution set" lies between 3 and 5, but does NOT include the endpoints 3 and 5.

Serggg [28]3 years ago
5 0

Hey there!


|2x -8|  < 2


This equation is a "and" problem


So, add 8 to both of your sides!


2x -8 +8


We get: 2x <  10


Divide by 2 to your sides


\frac{2x}{2} <  \frac{10}{2}  \\ \\ Cancel: \frac{2x}{2}  \\ \\ \\  Keep: \frac{10}{2} \\ \\ \\ \frac{10}{2}  =  5\\ \\ \\ Answer: x  < 5


Or you can use this add this part to your equation because this is a two step inequality


Add 8 to your sides again


2x - 8 +8 > -2 + 8 \\ \\ \\ Cancel: -8 + 8 \\ \\ \\ Keep: -2 + 8  \\ \\ \\ -2 + 8 = 6


We get: 2x > 6


Divide by 2 on each of your sides


\frac{2x}{2}  > \frac{6}{2}  \\ \\ \\ Cancel: \frac{2x}{2} \\ \\ \\ Keep: \frac{6}{2}  \\ \\ \\ x > 3


Answer: x< 5 and x> 3


Overall answer: C


Good luck on your assignment and enjoy day!


~LoveYourselfFirst:)


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