SOLUTION: -4*abs(2x-3)+7 = -1 I got no solution because absolute value cannot be negative. But, this is not the correct answer according to my classmate. Who is right?

Algebra ->  Algebra  -> Absolute-value -> SOLUTION: -4*abs(2x-3)+7 = -1 I got no solution because absolute value cannot be negative. But, this is not the correct answer according to my classmate. Who is right?       Log On

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

   

Question 133518: -4*abs(2x-3)+7 = -1
I got no solution because absolute value cannot be negative. But, this is not the correct answer according to my classmate. Who is right?
Answer by jim_thompson5910(21681) About Me  (Show Source):
You can put this solution on YOUR website!
-4%2Aabs%282x-3%29%2B7+=+-1+ Start with the given equation


-4%2Aabs%282x-3%29+=+-8+ Subtract 7 from both sides


abs%282x-3%29+=+2+ Divide both sides by -4. Notice how the right side is now positive. So this means that a solution exists.



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

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




Now lets focus on the first equation 2x-3=-2


2x=-2%2B3Add 3 to both sides


2x=1 Combine like terms on the right side


x=%281%29%2F%282%29 Divide both sides by 2 to isolate x



x=1%2F2 Reduce






Now lets focus on the second equation 2x-3=2



2x=2%2B3Add 3 to both sides


2x=5 Combine like terms on the right side


x=%285%29%2F%282%29 Divide both sides by 2 to isolate x



x=5%2F2 Reduce





So the solutions are:

x=1%2F2 and x=5%2F2