Question

Compare and Contrast: Two equations are listed below. Solve each equation and compare the solutions. Choose the statement that is true about both solution Equations Below in picture: A. Equation 1 has more solutions than equation 2 B. equation 1 and Equation 2 have the same number of solution C. Equation 2 has more solutions than Equation 1 D. the number of solutions cannot be determined

Answer 1

Solve each equation first and then choose the appropiate statement.

Equation 1

$|5x-6|=-41$

Since the absolute value of a number is always greater than 0 and -41<0, then this equation has no solutions.

Equation 2

$\begin{gathered} |7x+13|=27 \\ \Rightarrow7x+13=\pm27 \\ \Rightarrow7x=\pm27-13 \\ \Rightarrow x=\frac{\pm27-13}{7} \\ \Rightarrow x_1=\frac{27-13}{7}=\frac{14}{7}=2 \\ \Rightarrow x_2=\frac{-27-13}{7}=\frac{-40}{7} \\ \therefore x_1=2,x_2=-\frac{40}{7} \end{gathered}$

We can see that Equation 1 has 0 solutions and Equation 2 has 2 solutions.

Therefore, equation 2 has more solutions than equation 1.