Question

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

Answer 1

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.

Answer 2

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!

~$LoveYourselfFirst:)$