SOLUTION: Solve: 3+|2y-1|≥1. Graph the solution set on a number line.

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Question 379040: Solve: 3+|2y-1|≥1. Graph the solution set on a number line.
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
|2y - 1| >= 2

Case 1: 2y - 1 >= 2
2y >= 3
y >= 3/2

Case 2: -2y + 1 >= 2
-2y >= 1
y <= -1/2

-1..........-1/2..........0..........1/2..........1..........3/2..........2
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Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve: 3 + |2y-1| ≥ 1. Graph the solution set on a number line.
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            The solution by  @Penguin is  INCORRECT.

            I came to bring you a correct solution. 


You start with this inequality


    3 + |2y-1| >= 1.


Next you subtract the number 3 from both sides.


    |2y-1| >= 1 - 3,

or

    |2y-1| >= -2.


But the absolute value is ALWAYS NON-NEGATIVE number,

so the last inequality is valid FOR ANY VALUE of y.



ANSWER.  The solution set is the ENTIRE NUMBER LINE from -oo to oo.

Solved, answered, explained and completed.


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Ignore the post by  @Pinguin,  since it is   T O T A L L Y   W R O N G.