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?

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(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract 7 from both sides

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 , then or )

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

Now lets focus on the first equation

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Reduce

Now lets focus on the second equation

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Reduce

So the solutions are:

and

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