Question

Compare and Contrast: Below are two equations. Solve each equation and compare the two solutions. Choose the statement that is true about each solution. Equation #1 Equation #2 |2x - 4| = 5 |3x - 4| = -12 Equation #1 and Equation #2 have the same number of solutions. Equation #1 has more solutions than equation #2. Equation #1 has fewer solutions than equation #2. None of the statements above describe the number of solutions to equations shown.

Answer 1

Equation 1:

$|2x-4|=5$

This means:

$2x-4=5$ and $2x-4=-5$

Simplifying both the equations we get:

x = 4.5 and x = - 0.5

Equation 2:
$|3x-4|=-12$

There is no solution to this equation, as the modulus or absolute value of any expression can never be negative

Therefore, we can conclude that Equation 1 has more number of solutions that Equation 2.