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=(\pm27-13)/(7) \\ \Rightarrow x_1=(27-13)/(7)=(14)/(7)=2 \\ \Rightarrow x_2=(-27-13)/(7)=(-40)/(7) \\ \therefore x_1=2,x_2=-(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.