Question

Hey Guys <33 Can someone help me with this math question? Thank you if you do :))

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 |2x + 13| = 28
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.

I think C but I don't know :))

Answer 1

Both of these have the same number of solutions (which is 2)

Remember that |5x + 6| means "the absolute value of the expression '5x + 6'", so in this case, 5x + 6 could equal 41 or -41 since the absolute value would "strip away" the positive or negative sign and leave just the number

So, if you solve:
5x + 6 = 41
5x = 41 - 6 = 35
x = 35 / 5 = 7

5x + 6 = -41
5x = -41 - 6
5x = -47
x = -47 / 5

Do the same thing for the other expression:

2x + 13 = 28
2x = 28 - 13 = 15
x = 15 / 2

2x + 13 = -28
2x = -28 - 13
2x = -41
x = -41 / 2

So, both of these expressions have two solutions.

Hope this helps!

Good luck.