SOLUTION: |3b-2|=7

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Question 249356: |3b-2|=7
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%283b-2%29=7 Start with the given equation


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

3b-2=-7 or 3b-2=7 Set the expression 3b-2 equal to the original value 7 and it's opposite -7




Now lets focus on the first equation 3b-2=-7


3b=-7%2B2Add 2 to both sides


3b=-5 Combine like terms on the right side


b=%28-5%29%2F%283%29 Divide both sides by 3 to isolate b



b=-5%2F3 Reduce






Now lets focus on the second equation 3b-2=7



3b=7%2B2Add 2 to both sides


3b=9 Combine like terms on the right side


b=%289%29%2F%283%29 Divide both sides by 3 to isolate b



b=3 Divide





So the solutions to abs%283b-2%29=7 are:

x=-5%2F3 and x=3



Notice if we graph y=abs%283x-2%29 and y=7 (just set each side equal to y and graph), we get


graph%28500%2C500%2C-7%2C5%2C-10%2C10%2Cabs%283x-2%29%2C7%29 Graph of y=abs%283x-2%29 (red) and y=7(green)

and we can see the two graphs intersect at x=-5%2F3 and x=3. So this verifies our answer.