SOLUTION: How do you solve - 5| x + 1| = -10, whats the answer?

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Question 146867: How do you solve - 5| x + 1| = -10, whats the answer?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-5%2Aabs%28x%2B1%29=-10 Start with the given equation


abs%28x%2B1%29=2 Divide both sides by -5



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

x%2B1=-2 or x%2B1=2 Set the expression x%2B1 equal to the original value 2 and it's opposite -2




Now lets focus on the first equation x%2B1=-2


x=-2-1Subtract 1 from both sides


x=-3 Combine like terms on the right side






Now lets focus on the second equation x%2B1=2



x=2-1Subtract 1 from both sides


x=1 Combine like terms on the right side





So the solutions to -5%2Aabs%28x%2B1%29=-10 are:

x=-3 and x=1



Notice if we graph y=-5%2Aabs%28x%2B1%29 and y=-10 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-5%2C3%2C-12%2C8%2C-5%2Aabs%28x%2B1%29%2C-10%29 Graph of y=-5%2Aabs%28x%2B1%29 (red) and y=-10(green)

and we can see the two graphs intersect at x=-3 and x=1. So this verifies our answer.