Question

Need Help checking my answer, please!

Answer 1

yeah

Answer 2

i'm here

Answer 3

\[\left| 2x1 \right|\le 11\]

Answer 4

what does 1 after x means?

Answer 5

I got:
\[x \le 5 or x \ge 5\]

Answer 6

Sorry..(2x+1)

Answer 7

oh

Answer 8

When solving an absolute inequality of this type, you need to change the absolute value inequality into a compound inequality (without absolute value signs.)

Answer 9

So, 2x+1=11
which would make x=5

Answer 10

\(|X|\le k\)

Here, X stands for an expression in x, and k is a non-negative number.

Solve this compound inequality:

\(-k \le X \le k\)

Answer 11

N ow we look at your absolute value inequality.

\(|2x + 1| \le 11\)

It becomes:

\(-11 \le 2x + 1 \le 11\)

Now we solve the compound inequality.

Subtract 1 from all 3 sides:

\(-12 \le 2x \le 10\)

Divide all 3 sides by 2:

\(-6 \le x \le 5\)

Which means the same as

\(x \ge -6\) and \(x \le 5\)

Answer 12

Oh, thank you! That helps so much!

Answer 13

You're welcome.
If the absolute value inequality has a \(\gt\) or a \(\ge\), then this is what you do:

\(|X| \gt k\)

becomes

\(X \lt -k\) or \(X \gt k\)

In this case, the compound inequality has the word "or" instead of "and".