Question 166070: 2[d + 3] = 8
The bar is a straight line, and I don't know how to type it. It is called the
absolute bar.
THanks for your help!
Answer by midwood_trail(310)   (Show Source):
You can put this solution on YOUR website! To solve an absolute value equation, isolate the absolute value on one side of the equal sign, and establish two cases:
Case One:
Set the expression inside the
absolute value symbol equal to
the other given expression.
Case Two:
Set the expression inside the
absolute value symbol equal to
the negation of the other given
expression
Your question:
2|d + 3| = 8
We want to isolate the absolute value first.
We divide both sides by 2 to get this done.
|d + 3| = 8/2
|d + 3| = 4
We now establish two cases as written above.
Case One:
d + 3 = 4
d = 4 - 3
d = 1
Case Two:
d + 3 = -4
d = -4 - 3
d = -7
Now, you must check. The two cases create "derived" equations. These derived equations may not always be true equivalents to the original equation. Consequently, the roots of the derived equations MUST BE CHECKED in the original equation so that you do not list extraneous roots as answers.
We plug our answers of d = 1 and d = -7 in the original absolute value equation given to see which will create the same answer on both sides of the equation.
Let d = 1
2|1 + 3| = 8
2|4| = 8
2(4) = 8
8 = 8...It checks!!
We now let d = -7
2|-7 + 3| = 8
2|-4| = 8
2(4) = 8
8 = 8...It also checks!!
So, our final answer is: d = 1 and d = -7
Did you follow?
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