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 <2 + 8 \\ \\ CancelOut: -8 and 8 \\ \\ Keep: 2 +8 \\ \\ \\ 2x = 2x \\ \\ \\ 2 + 8 = 10`

We get:
`2x < 10`

Divide by
`2` to your sides

`(2x)/(2) < (10)/(2) \\ \\ Cancel: (2x)/(2) \\ \\ \\ Keep: (10)/(2) \\ \\ \\ (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

`(2x)/(2) > (6)/(2) \\ \\ \\ Cancel: (2x)/(2) \\ \\ \\ Keep: (6)/(2) \\ \\ \\ x > 3`

Answer:
`x< 5` and
`x> 3`

Overall answer:
`C`

Good luck on your assignment and enjoy day!

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`LoveYourselfFirst:)`