SOLUTION: solve: |2w + 4| = 6 wouldn't w = 1 or w = -1 this one seems too simple, or am I right?

Algebra ->  Absolute-value -> SOLUTION: solve: |2w + 4| = 6 wouldn't w = 1 or w = -1 this one seems too simple, or am I right?       Log On


   

Question 42905: solve:
|2w + 4| = 6
wouldn't w = 1 or w = -1
this one seems too simple, or am I right?
Found 2 solutions by aaaaaaaa, tutorcecilia:
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
Be careful! If w = -1, -2 + 4 = 2, not -6. Your second solution would have to be w = -5. Substituting
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: 2w%2B4 simplifies to -6
  • Text form: 2w+4 simplifies to -6
  • Cartoon (animation) form: simplify_cartoon%28+2w%2B4+%29
    For tutors: simplify_cartoon( 2w+4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2Ahighlight_red%28+w+%29%2B4.
Replaced w with -5
It becomes 2%2Ahighlight_green%28+-5+%29%2B4.
Look at highlight_red%28+2%2A-5+%29%2Bhighlight_red%28+4+%29.
Replace constants in expression: highlight_red%28+2%2A-5+%29,highlight_red%28+4+%29 with highlight_green%28+-6+%29
It becomes highlight_green%28+-6+%29.
Look at highlight_red%28+-6+%29.
Removed extra sign in front of -6
It becomes -highlight_green%28+6+%29.
Result: -6

Universal Simplifier and Solver


Done!

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
With absolute values you are looking at distances away from zero on the number line. Is the distance to the right (positive) or to the left (negative) of zero? Since we do not know the direction of the distance, we must use two equations. One equation in case the number is to the right of zero. And the other equation in case the number is to the left of zero.
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So the problem is set up as:
2w + 4 = +-(6) (positive and negative 6)
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First, use the positive 6
2w+4=+6
2w=6-4
2w=2
w=1
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Check the answer when w=1:
|2(1) + 4| = 6
|6| = 6
6=6 Therefore this is a true statement
.
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Second, use the negative 6
2w+4=-6
2w=-6-4
2w=-10
w=-5
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.Checking that w=-5
|2(-5) + 4| = 6
|-10+ 4| = 6
|-6| = 6
6=6 is a true statement, so w=-5