Absolute Values (part 2)
Now let’s do a comparison problem involving absolute values What? You may be thinking. That’s like a Frankenproblem, a riddle within a riddle. You have mastered the skills needed to solve it, trust me.
Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Primarily this is a comparison problem, since at the end of the day, we need to compare Quantity A and Quantity B. So let’s run through our Steps to Success for comparison problems.
Step 1: What don’t we know? We don’t know x.
Step 2: Get the unknown to one side. How convenient, that’s already been done. x is only on one side of the equation of 4|x - 3| = 8
Step 3: If there is an absolute value in the problem, get it alone to one side.
Well there is an absolute value in this problem. It’s not all alone on the left-hand side, because outside of the absolute value brackets is a 4.
We have to take care of that. Since the 4 is being multiplied by the absolute value, we should divide both sides by 4.
This is looking familiar! Now we have a plain old absolute value problem. Let’s follow the Steps to Success for Solving Absolute Value problems.
Step 1: Write the equation twice without the absolute value bars.
Step 2: With one of the equations, for everything that was inside the absolute value bars, change the sign to the opposite.
Step 3: Solve each equation for the unknown. Let’s start with the top equation.
Now let’s solve the bottom equation of x – 3 = 2
Okay, so our two answers are x = 1 and x = 5.
Step 4: Check your work! Substitute the answers you got back into the original equation.
We now know what x is worth. x = 1 and x = 5. On a number line it looks like this:
Now that we’ve solved for x, the unknown, let’s remind ourselves what the question even was.
Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices:
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Notice I jotted under Quantity A the values for x, since we went to all that work to find them!
A number line could be useful. Quantity A is still in green, Quantity B is in purple.
What is our answer? Is Quantity A greater? No, it’s not worth more than Quantity B.
Is Quantity B greater? No, it’s not always worth more than Quantity A.
Are the two quantities equal? Not always. They could both be worth 5, but Quantity A is also worth 1, which isn’t equal to 5. In short, we just don’t know. That brings us to option D – D for don’t know!
The relationship cannot be determined from the information given. Choice D.
It may feel unsettling to do all that work just to determine you don’t know. But just remember, your goal is to answer a GRE question correctly, which you just did! Great job!