SOLUTION: Solve each absolute value equation |2x-5|-12=-5

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Question 174185This question is from textbook algebra 1
: Solve each absolute value equation
|2x-5|-12=-5 This question is from textbook algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
abs%282x-5%29-12=-5 Start with the given equation


abs%282x-5%29=7 Add 12 to both sides.


Break up the absolute value (remember, if you have abs%28x%29=a, then x=-a or x=a)

2x-5=-7 or 2x-5=7 Set the expression 2x-5 equal to the original value 7 and it's opposite -7




Now lets focus on the first equation 2x-5=-7


2x=-7%2B5Add 5 to both sides


2x=-2 Combine like terms on the right side


x=%28-2%29%2F%282%29 Divide both sides by 2 to isolate x



x=-1 Divide






Now lets focus on the second equation 2x-5=7



2x=7%2B5Add 5 to both sides


2x=12 Combine like terms on the right side


x=%2812%29%2F%282%29 Divide both sides by 2 to isolate x



x=6 Divide





So the solutions are:

x=-1 or x=6



Notice if we graph y=abs%282x-5%29-12 and y=-5 (just set each side equal to y and graph), we get


Graph of y=abs%282x-5%29-12 (red) and y=-5(green)

and we can see the two graphs intersect at x=-1 and x=6. So this verifies our answer.