A friend of mine posted this on another website, and the answer eludes me, too. Can one of you spoofee geniuses help?
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I used to be pretty good at math, but I was just looking a sample question from the SAT, and for the life of me, I can't figure out the answer, even when it's explained. Here's the question:
1. |4x - 7| = 5
|3 - 8x| = 1
What value of x satisfies both of the equations above?
And here's the answer and the explanation:
Since |4x - 7| = 5
the value of |4x - 7| is either 5 or -5
4x-7=5 or 4x - 7 = -5
4x=12 4x = 2
x=3 x = 1/2
The two values of x that satisfy the first equation are 3 and 1/2
Since 3-8x=1 the value of 3-8x is either 1 or -1
3 - 8x =1 or 3 - 8x = -1
8x + 2 8x = 4
x = 1/4 x = 1/2
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
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Here are the things that have me confused:
(1) If |4x - 7| = 5, then how can the value of |4x - 7| be either 5 or -5?
(2) Similarly, if 3-8x=1, then how can the value of 3-8x be either 1 or -1?
(I edited this to correct a typo in the original posting.)