SOLUTION: 2|d+3|=8

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Question 106713This question is from textbook Algebra 1
: 2|d+3|=8 This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2%2Aabs%28d%2B3%29=8 Start with the given equation


abs%28d%2B3%29=4 Divide both sides by 2



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

d%2B3=-4 or d%2B3=4 Set the expression d%2B3 equal to the original value 4 and it's opposite -4




Now lets focus on the first equation d%2B3=-4


d%2B3=-4 Start with the given equation


d=-4-3Subtract 3 from both sides


d=-7 Combine like terms on the right side

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Answer:
So our answer is d=-7




Now lets focus on the second equation d%2B3=4



d%2B3=4 Start with the given equation


d=4-3Subtract 3 from both sides


d=1 Combine like terms on the right side

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Answer:
So our answer is d=1



So the solutions to 2%2Aabs%28d%2B3%29=8 are:

x=-7 and x=1



Notice if we graph y=2%2Aabs%28x%2B3%29 (just replace d with x) and y=8 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-9%2C3%2C-10%2C10%2C2%2Aabs%28x%2B3%29%2C8%29 Graph of y=2%2Aabs%28x%2B3%29 (red) and y=8(green)

and we can see the two graphs intersect at x=-7 and x=1. So this verifies our answer.