Question: Find the Value

Comment on Find the Value

Can we Isolate 2x in the equation and solve further, as we are asked for the value of 2x?
greenlight-admin's picture

With that approach, I believe you'll find that you're unable to eliminate all of the variables you need to eliminate in order to enter a numeric answer.

That said, perhaps you can show me your solution.

Can we check only the right side of the equation ONLY in general when we have the square root on the left side ? I mean once we realized that the right side is negative then we should immediately exclude this solution without having to check the left side that has the square root. i.e Can we apply this role always to all equations that has the square root on the left side? Thanks!
greenlight-admin's picture

You can actually do either side.

If the part under the square root turns out to be negative, then we know we have an extraneous root.

Conversely, if the right side (the part NOT under the square root) turns out to be negative, then we also know we have an extraneous root.

However, if we evaluate just one side and find that it evaluates to be POSITIVE, then we need to evaluate the other side as well.

Sounds great! Thanks.

when we subtract 3x² from both sides, how come we get x²?
greenlight-admin's picture

On one side, we have 3x² and on the other side we have 4x²
So, if we subtract 3x² from both sides, we get 4x² - 3x² on the right side.

4x² - 3x² = x²

Does that help?


When exactly do you have to check for extraneous roots? When there's equations with square roots, powers, and quadratic/quadratic questions? I always forget :(
greenlight-admin's picture

On the GRE, extraneous roots can appear in equations involving absolute value and equations involving square roots.

Hi Brent,

I encountered this question on the GRE prep club website:

For the following question, select all the answer choices that apply.

What are the possible values for the slope of a line passing through point (–1, 1) and passing in between points (1, 3) and (2, 3) but not containing either of them?

(c) 3/4

What's the way out?

greenlight-admin's picture

Question link:

The key concept here is that the line passes BETWEEN points (1, 3) and (2, 3)
So, if we find the slope from (–1, 1) to (1, 3) and the slope from (–1, 1) to (2, 3), then the slope of the line must be BETWEEN the two slopes we calculated.

Does that help?


Hi Brent,

I finally approached this question. In the first place, the rational numbers in the answer choices got me worried.

Nevertheless, I solved for 2 slopes: between (-1,1) and (1,3). The value of 'm' in this case is 1.

For (-1,1) and (2,3), the value of 'm' is 2/3 or 0.66.
So, we are looking for values that are between 0.66 and 1.

I then converted the answer choices: 1/2 is 0.5
3/5 is 0.66 and 3/4 is 0.75. Therefore, answer choices A and B are the possible values for the slope since they are between 0.66 and 1.

Does it make any sense?

greenlight-admin's picture

The first part of your solution is correct, but there are some errors after that.

You're correct to say that the correct answers will have values that are BETWEEN 0.6666... and 1.
Let's check the answer choices

(A) 1/2 = 0.5
0.5 is not BETWEEN 0.6666... and 1.
Eliminate A

(B) 3/5 = 0.6
0.6 is not BETWEEN 0.6666... and 1.
Eliminate B

(C) 3/4 = 0.75
0.75 IS BETWEEN 0.6666... and 1.
Keep C

Answer: C


What's a method to deciding early on in the problem if the easiest way to answer the question is by solving for x all the way or if there's another hidden indicator that's easier?
greenlight-admin's picture

I'm not 100% sure what you mean by "solving for x all the way."

Are you referring to the practice question that asks for the value of 2x (instead of just x)?
If that's what you're asking, then my advice is to solve the question for x, BUT watch out for the possibility that 2x appears at some point in the solution.

Consider this example:
If x² - 3x + 11 = x² - 5x + 4, then what is the value of 2x?
We might start by subtracting x² from both sides to get: -3x + 11 = -5x + 4
Now add 5x to both sides: 2x + 11 = 4
Aha, 2x has appeared in our solution!
From here, if we subtract 11 from both sides for yet: 2x = -7
At this point it would make no sense to continue solving this equation for x, since we already know that 2x = -7, and our goal is to find the value of 2x.

Does that help?

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