SOLUTION: Solve each absolute value equation a. |x-5|=3

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Question 174181This question is from textbook algebra 1
: Solve each absolute value equation
a. |x-5|=3 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%28x-5%29=3 Start with the given equation


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

x-5=-3 or x-5=3 Set the expression x-5 equal to the original value 3 and it's opposite -3




Now lets focus on the first equation x-5=-3


x=-3%2B5Add 5 to both sides


x=2 Combine like terms on the right side






Now lets focus on the second equation x-5=3



x=3%2B5Add 5 to both sides


x=8 Combine like terms on the right side





So the solutions to abs%28x-5%29=3 are:

x=2 and x=8



Notice if we graph y=abs%28x-5%29 and y=3 (just set each side equal to y and graph), we get


Graph of y=abs%28x-5%29 (red) and y=3(green)

and we can see the two graphs intersect at x=2 and x=8. So this verifies our answer.