Solving for X in Absolute Value equations

[LoreneTJ]

Hello Math Help! I could use some help solving for X with an absolute value equation. My math is correct but I'm doing something wrong regarding negative signs. I'll use [ ] for the absolute value bars. The problem is as follows:
negative [2x-1] is greater than or equal to negative 3. (The negative sign is outside the absolute value bars.)
For the first scenario this is what I've done:
negative 2x - 1 is greater than or equal to negative 3
negative 2x is greater than or equal to negative 2
answer: x is greater than or equal to positive 1.

For the second scenario this is what I've done:
negative 2x - 1 is Less than or equal to positive 3
negative 2x is less than or equal to positive 4
answer: x is less than or equal to negative 2

According to the answers in my book, my answers (negative 2, positive 1) are incorrect. The answers are (negative 1, positive 2). I could really use your help!
thanks,
LoreneTJ

 

[mmm4444bot]

… My math is correct but I'm doing something wrong regarding negative signs.

Hi Lorene:

If you're doing something wrong with a negative sign, then your math is not correct.

I would start by multiplying both sides of the original inequality by -1.

|2x - 1| <= 3

If we interpret absolute value as the distance from zero on the number line, then the following rule for removing the absolute value symbols is clear.

Given: |expression| < constant

Write: -constant < expression < constant

If we apply this reasoning to the inequality above, then we get:

-3 <= 2x - 1 <= 3

Try solving this one for x.

Also, I do not agree with your text's answer because the solution set is a closed interval.

In other words, the interval notation needs square brackets [-1, 2] to show that the endpoints are included.

 

[LoreneTJ]

Thanks--It worked like a charm!