Question

Solve and graph the absolute value inequality: |4x + 1| ≤ 5

number line with closed dots on −1.5 and 1 with shading going in the opposite directions.

number line with open dots on −1.5 and 1 with shading in between.

number line with closed dots on −1 and 1 with shading in between.

number line with closed dots on −1.5 and 1 with shading in between.

Last question for the night lol

Answer 1

You do realize that |4x + 1| ≤ 5 is equivalent to

-5 < 4x + 1 < 5

right?

Answer 2

And in general

|ax - b| < c is equivalent to

-c < ax - b < c

Answer 3

|ax + b| < c is equivalent to

-c < ax + b < c

Answer 4

In either case you can isolate x with any compound inequality.

Answer 5

I hope I didn't confuse you too much.

Answer 6

@Lena772 say something...lol

Answer 7

no i'm just thinking about everything lol sorry

Answer 8

I think it's A because when I solve the absolute values I get -1.5 <=x and x<=1

Answer 9

And the equal sign means a closed circle

Answer 10

or maybe it's d because i can rewrite it as -1.5<=x<=1

Answer 11

I know it's not B or C

Answer 12

I may have confused you with my mistake in the equalties

Answer 13

You do realize that |4x + 1| ≤ 5 is equivalent to -5 ≤ 4x + 1 ≤ 5

Answer 14

-6<=4x<=4
-1.5<=x<=1

Answer 15

So D?

Answer 16

Yes that will be correct.

Answer 17

If you start wth a compound inequalty, you should end wth a compound inequality. .

Answer 18

so

-5 ≤ 4x + 1 ≤ 5 becomes -1.5 ≤ x ≤1

Answer 19

If you have a compound inequality it is best to try to stick with it as much as possible while solving

Answer 20

Well, at least you are done with everything.