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|5t - 7| = 11

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2 Answers

Let's start with definition of absolute value
1. l a l = a , if a ≥ 0 (if "a" is positive or 0) , for example 
    l 5 l = 5
2. l a l = -a , if a < 0 (if "a" is negative) , for example
   l -5 l = - (-5) = 5     So, absolute value is always positive or zero.
So, we need to consider two cases, because expression contain variable and can be positive, or negative
1. Let's assume that (5t - 7) ≥ 0 , then 5t - 7 = 11 ---> 5t = 18 ---> t1 = 18/5
2. If (5t - 7) < 0 , then we have to put the "–" before (5t - 7)
  – (5t - 7) = 11 or we can write 5t - 7 = -11 ---> 5t = -4 ---> t2 = - 4/5
Now let's check our answer l 5 · (18/5) - 7 l = 11
                                                        11    = 11 
                                         l 5 · (-4/5) - 7 l = 11
                                                         11    = 11

Since |+/-11| = 11, there are two solutions for 5t-7.

5t-7 = 11 => t = 18/5

or

5t-7 = -11 => t = -4/5

Answer: t = 18/5 or -4/5