SOLUTION: Consider the following absolute value equation. |5x + 9| − 3 = 13 Write two equivalent equations that do not contain an absolute value symbol. (Select all that apply.) A.5x +

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Question 1191105: Consider the following absolute value equation.
|5x + 9| − 3 = 13
Write two equivalent equations that do not contain an absolute value symbol. (Select all that apply.)
A.5x + 3 = 22
B.5x + 9 = 16
C.5x + 9 = −16
D.5x − 9 = 16
E.5x − 3 = −22
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is 5x+9-3=13 or 5x+9=16. Just take off the brackets and solve normally for the first one.
The second one has to have the opposite side negated when you take off the brackets.
That is B and C
so |5x+9|=16
5x+9=-16
5x=-25
x=-5
so solutions are x=1.4 and -5
B is one choice
C is the other choice, which is consistent with the statement above.
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

The given equation  

    |5x+9| - 3 = 13    (1)


is the same as the absolute value equation

    |5x+9| = 16        (2)    (a canonical form of a linear absolute value equation).



This last equation is equivalent to the system of two equations


    5x+9 = 16          (3)

or

    5x+9 = -16,        (4)


connected by the service word OR.


Thus the given equation is equivalent to the system of two equations  (B)  and  (C),  connected with the service word OR.


It means that the set of solutions to equation (1) is the union of the sets of solutions to equations  (3)  and  (4).

Solved, answered and explained.



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