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|5t - 7| = 11

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3 Answers

Solving for variable "t".
5t -7 = 11

Move all terms containing t to the left, all other terms to the right.

Add '7' to each side of the equation.
5t -7 + 7 = 11 + 7

Combine like terms: -7 + 7 = 0
5t + 0 = 11 + 7
5t = 11 + 7
5t = 18

Divide each side by '5'.
5t/5 = 18/5

Simplifying
t = 3 3/5
t = 3.6

Comments

The other half of this problem is..
 
-(5t -7) = 11
-5t + 7 = 11
-5t +7 -7 = 11 - 7
-5t = 4
-5t/-5 = 4/-5
t  = -4/5
 
Absolute value of t = 3 3/5  and -4/5
 
 

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