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 |2x + 13| = 28

a.Equation 1 has more solutions than equation 2.

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

c.Equation 2 has more solutions than Equation 1.

d.The number of solutions cannot be determined

Answer 1

Do you know the 1st step to solving absolute value equations?

Answer 2

\[
|5x+6| = 41 \\
[-(5x+6)]^2 = (5x+6)^2 = (|5x+6|)^2 \\
(5x+6)^2 = 41^2 \\
25x^2 + 60x +36 = 1681 \\
25x^2 +60x - 1645 = 0 \;// \div 5\\
5x^2 + 12x - 329 = 0 \\
x_{1,2} = \frac{ -12 \pm \sqrt{12^2 - 4\cdot5\cdot(-329)} }{2 \cdot 5} = \frac{ -12 \pm \sqrt{144 + 6580} }{10} \\
x_{1,2} = \frac{ -12 \pm \sqrt{6724} }{10} = \frac{ -12 \pm 82 }{10}\\
x_1 = \frac{-12 + 82}{10} = \frac{70}{10} = 7 \\
x_2 = \frac{-12 - 82}{10} = - \frac{94}{10} = -9.4
\]
Hope I got it right.
Anyway that's for first equation. now try second