SOLUTION: solve |2x-7|=12, show all work

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: solve |2x-7|=12, show all work      Log On

Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

   

Question 198054: solve |2x-7|=12, show all work
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
abs%282x-7%29=12 Start with the given equation


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

2x-7=-12 or 2x-7=12 Set the expression 2x-7 equal to the original value 12 and it's opposite -12




Now lets focus on the first equation 2x-7=-12


2x=-12%2B7Add 7 to both sides


2x=-5 Combine like terms on the right side


x=-5%2F2 Reduce




Now lets focus on the second equation 2x-7=12



2x=12%2B7Add 7 to both sides


2x=19 Combine like terms on the right side


x=%2819%29%2F%282%29 Divide both sides by 2 to isolate x



x=19%2F2 Reduce





So the solutions to abs%282x-7%29=12 are:

x=-5%2F2 and x=19%2F2