SOLUTION: |5x|+4=10 |a+1|=|a-8|

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Question 1127147: |5x|+4=10
|a+1|=|a-8|
Found 2 solutions by josgarithmetic, addingup:
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
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|5x|+4=10


|a+1|=|a-8|
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Two very separate equations, not of a system.


abs%28a%2B1%29=abs%28a-8%29

(*)
a%2B1=-a%2B8
2a=7
a=7%2F2

(*)
a%2B1=a-8
no solution here

The only solution possible is a=7%2F2=3%261%2F2



graph%28400%2C400%2C-5%2C8%2C-5%2C8%2Cabs%28x%2B1%29%2Cabs%28x-8%29%29



check:
abs%283%261%2F2%2B1%29=abs%283%261%2F2-8%29
4%261%2F2=4%261%2F2

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
|5x|+ 4 = 10
|5x|+ 4 + − 4 = 10 + − 4
|5x| = 6
5x = 6 or 5x = −6
x = 6/5 or x = -6/5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|a + 1| = |a - 8|
either a + 1 = a − 8 or a + 1 = −(a − 8)
a + 1 = a − 8 (Possibility 1)
subtracta from both sides:
1 = − 8
Subtract 1 from both sides:
1 - 1 = -8 -1
0 = -9 This is the first possibility. Let's explore the second possibility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
a + 1 = −(a − 8)
a + 1 = − a + 8
2a + 1 = 8
2a + 1 − 1 = 8 − 1
2a = 7
2a/2 = 7/2 (Divide both sides by 2)
a = 7/2 I like this answer better, try it in the equation if you want to check.