Hey there!
[tex] |2x -8| < 2 [/tex]
This equation is a "and" problem
So, add [tex] 8 [/tex] to both of your sides!
[tex] 2x -8 +8 <2 + 8 \\ \\ CancelOut: -8 and 8 \\ \\ Keep: 2 +8 \\ \\ \\ 2x = 2x \\ \\ \\ 2 + 8 = 10 [/tex]
We get: [tex] 2x < 10 [/tex]
Divide by [tex] 2 [/tex] to your sides
[tex] \frac{2x}{2} < \frac{10}{2} \\ \\ Cancel: \frac{2x}{2} \\ \\ \\ Keep: \frac{10}{2} \\ \\ \\ \frac{10}{2} = 5\\ \\ \\ Answer: x < 5 [/tex]
Or you can use this add this part to your equation because this is a two step inequality
Add [tex] 8 [/tex] to your sides again
[tex] 2x - 8 +8 > -2 + 8 \\ \\ \\ Cancel: -8 + 8 \\ \\ \\ Keep: -2 + 8 \\ \\ \\ -2 + 8 = 6 [/tex]
We get: [tex] 2x > 6 [/tex]
Divide by [tex] 2 [/tex] on each of your sides
[tex] \frac{2x}{2} > \frac{6}{2} \\ \\ \\ Cancel: \frac{2x}{2} \\ \\ \\ Keep: \frac{6}{2} \\ \\ \\ x > 3 [/tex]
Answer: [tex] x< 5[/tex] and [tex] x> 3 [/tex]
Overall answer: [tex] C [/tex]
Good luck on your assignment and enjoy day!
~[tex] LoveYourselfFirst:) [/tex]
