SOLUTION: I'm not sure what type of equation this is, but I need help on how the answer was found. I am taking an SAT soon, and this is an example in my test booklet. I don't know how they

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Question 262223: I'm not sure what type of equation this is, but I need help on how the answer was found. I am taking an SAT soon, and this is an example in my test booklet. I don't know how they found the answers for these equations, can you please help me find out how to find the answer on my own?
Question:
What value of X satisfies both of the equations below?
|4x-7|=5 and |3-8x|=1
Since |4x-7|=5, the value of 4x-7 is either 5 or -5.
4x-7=5 4x-7=-5
4x=12 Or 4x=2
x=3 x=1/2
(I don't see how 4x=12, x=3, 4x=2, etc...)
Since |3-8x|=1, the value of 3-8x is either 1 or -1.
3-8x=1 3-8x=-1
8x=2 Or 8x=4
x=1/4 x=1/2
(again, I don't know how they got the answers for
the equations.)
The two values of x that satisfy the second equation are 1/4 and 1/2. You are asked to find the value of x that satisfies BOTH equations. That value is 1/2. The answer can be entered in the grid as 1/2 or .5.
I would appreciate some help on how they found the answers for the equations because I have no idea how this was answered.

Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!
What value of X satisfies both of the equations below?
(i)
(ii)
here are my steps:
set (i) = 5 and then -5. solve for x.

add 7 to both sides to get

divide by 4 on both sides to get

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add 7 to both sides to get

divide by 4 to get

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Now we look at (ii).
setting it = 1 or -1, solving for x, we get

subtract 3 from both sides to get

divide by -8 to get

--

subtract 3 from both sides to get

divide by -8 to get

--
Now looking at our answers we see that x = 1/2 is the same. So it is the answer we need.