SOLUTION: Whats the answer to |2x + 6| - 4 = 20?

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Question 146868: Whats the answer to |2x + 6| - 4 = 20?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%282x%2B6%29-4=20 Start with the given equation


abs%282x%2B6%29=24 Add 4 to both sides.


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

2x%2B6=-24 or 2x%2B6=24 Set the expression 2x%2B6 equal to the original value 24 and it's opposite -24




Now lets focus on the first equation 2x%2B6=-24


2x=-24-6Subtract 6 from both sides


2x=-30 Combine like terms on the right side


x=%28-30%29%2F%282%29 Divide both sides by 2 to isolate x



x=-15 Divide






Now lets focus on the second equation 2x%2B6=24



2x=24-6Subtract 6 from both sides


2x=18 Combine like terms on the right side


x=%2818%29%2F%282%29 Divide both sides by 2 to isolate x



x=9 Divide





So the solutions to abs%282x%2B6%29-4=20 are:

x=-15 and x=9



Notice if we graph y=abs%282x%2B6%29-4 and y=20 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-17%2C11%2C-3%2C21%2Cabs%282x%2B6%29-4%2C20%29 Graph of y=abs%282x%2B6%29-4 (red) and y=20(green)

and we can see the two graphs intersect at x=-15 and x=9. So this verifies our answer.