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.

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.

danjs · Answer

are you familiar with the absolute value ?

sparklestaraa · Answer

hmmm no not much but i think it is 	Equation #1 has more solutions than equation #2.

danjs · Answer

how did you arrive there

sparklestaraa · Answer

actually to be honest i just figured it was that answer because 3x-4 is larger than the other one so i thought maybe its reverse psychology

danjs · Answer

From the above, you see there are 2 solutions to the first...

sparklestaraa · Answer

always like no matter what the equation is

danjs · Answer

an absolute value, is like a magnitude of distance from the origin, you cant have a negative value for the magnitude

danjs · Answer

$$\left| -x \right| = x$$

sparklestaraa · Answer

ohhhh

danjs · Answer

now if there were a negative in front of the absolute value , it is possible
$$-\left| -x \right| = -x$$

danjs · Answer

so how many solutions does equation 2 have?

danjs · Answer

$$\left| 3x-4 \right| = -12~~~~~~false$$

sparklestaraa · Answer

ohhhh ok :D