Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions.

Equation 1 Equation 2
|5x − 6| = −41 |7x + 13| = 27
Equation 1 has more solutions than equation 2.

Equation 1 and Equation 2 have the same number of solutions.

Equation 2 has more solutions than Equation 1.

The number of solutions cannot be determined.

Question

Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solutions.

Equation 1	Equation 2
|5x − 6| = −41	|7x + 13| = 27
 Equation 1 has more solutions than equation 2.

 Equation 1 and Equation 2 have the same number of solutions.

 Equation 2 has more solutions than Equation 1.

 The number of solutions cannot be determined.

anonymous · Answer

I have clue what to do for this one...

anonymous · Answer

*no clue

ganeshie8 · Answer

Can absolute value of something ever be negative ?

anonymous · Answer

No. Doesn't it always convert to positive?

ganeshie8 · Answer

Right, absolute value measures the distance. Distances are always nonnegative

anonymous · Answer

Oh, okay.

ganeshie8 · Answer

based on that info, what can you conclude about the solutions of first equation :

|5x − 6| = −41

?

anonymous · Answer

Um...I honestly don't know. Find solutions?

ganeshie8 · Answer

|5x − 6| = −41

it says absolute value equals some negative value, but earlier we have argued that absolute value can never be negative, so.... ?

anonymous · Answer

So, it's really +41 @ganeshie8

ganeshie8 · Answer

Nope, its an impossible statement.
so there are no solutions for the first equation

ganeshie8 · Answer

But the second equation has two solutions

anonymous · Answer

Okay, so that means it's C. Would you mind showing me how to solve the second equation @ganeshie8 ?

ganeshie8 · Answer

Correct!

anonymous · Answer

Thank you so much! :)