SOLUTION: I am supposed to solve this inequality and write the answer in interval notation but I am stuck! Here is what I have so far: |2x – 1| + 10 ≥ 5 |2x – 1| + 10-10 ≥ 5-1

Algebra ->  Inequalities -> SOLUTION: I am supposed to solve this inequality and write the answer in interval notation but I am stuck! Here is what I have so far: |2x – 1| + 10 ≥ 5 |2x – 1| + 10-10 ≥ 5-1      Log On


   

Question 1000779: I am supposed to solve this inequality and write the answer in interval notation but I am stuck! Here is what I have so far:
|2x – 1| + 10 ≥ 5
|2x – 1| + 10-10 ≥ 5-10
|2x – 1|≥-5
2x-1≥5, 2x-1≤-5
2x-1+1≥5+1, 2x-1+1≤-5+1
2x≥6, 2x≤-4
2x/2≥6/2, 2x/2≤-4/2
x≥3, x≤-2
What am I supposed to do after this?
Thank you in advance for your help.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The absolute value will not be greater than or equal to negative five; because absolute values are never negative. Your step giving abs%282x-1%29%3E=-5 is not very meaningful in the way it is written. If referring to negative 5, the right member needs to be non-negative, so maybe choose 0 for the right member; otherwise the statement would not make good sense.

TRY see what happens if right member still -5.
If 2x-1 is non-negative, then 2x-1%3E=-5
2x%3E=-5%2B1
2x%3E=-4
x%3E=-2
If 2x-1 is negative, then -2x%2B1%3E=-5
-2x%3E=-5-1
-2x%3E=-6
x%3C=3
-
Those would seem to say that the solution would be highlight_green%28-2%3C=x%3C=3%29. Will all of the points any one at a time work in the original inequality?

Negative 1 is one of the values in the apparent solution. Test it! Does it work?
abs%282x-1%29%2B10%3E=5
abs%282%28-1%29-1%29%2B10%3E=5
abs%28-2-1%29%2B10%3E=5
3%2B10%3E=5
13%3E=5-------This seemed to work.

Test negative 2.
abs%282%28-2%29-1%29%2B10%3E=5
abs%28-4-1%29%2B10%3E=5
15%3E=5-----------this also works.

In fact, no matter what value x you choose, it will work in the original inequality, even outside of the "solved" interval.

SOLUTION: ALL REAL NUMBERS!

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
I am supposed to solve this inequality and write the answer in interval notation but I am stuck! Here is what I have so far:
|2x – 1| + 10 ≥ 5
|2x – 1| + 10-10 ≥ 5-10
|2x – 1|≥-5
2x-1≥5, 2x-1≤-5
2x-1+1≥5+1, 2x-1+1≤-5+1
2x≥6, 2x≤-4
2x/2≥6/2, 2x/2≤-4/2
x≥3, x≤-2
What am I supposed to do after this?
Thank you in advance for your help.
Observe the inequality!

If you OMIT the |2x - 1| from the left side of the inequality, you' ll see that the inequality is still true, as: 10+%3E=+5. 

Thus, no matter what value you substitute for x, the left side will increase further, as you'll get a value that's > 10. 

Therefore, the solution, in interval notation is: (highlight_green%28-+infinity%29,highlight_green%28infinity%29)