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

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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(39618)   (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 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



If 2x-1 is negative, then



-
Those would seem to say that the solution would be . 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?




-------This seemed to work.

Test negative 2.


-----------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(10552)   (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: . 

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: (,) 

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