What number line could be the solution?
The GREs won’t give you unsolvable problems. Any problem you see is possible to answer. And you will be able to answer it, because of all of your studying!
Here is such a problem:
You may notice the only number on the numbers lines is zero. Are these people crazy? you may be thinking. Who can solve a math problem without numbers?
The problem is solvable, and I’m so glad you are seeing it for the first time now, so you can see it’s actually not very tricky. Let’s tackle the inequality.
We see this equality has the f word: fractions. Ugh, who wants to deal with a fraction? We don’t, so we’ll get rid of it right away. Multiply both sides by 3.
On the right side the 3s cancel out top and bottom, on the left side we distribute the 3. (A fancy way of saying: we multiply every single term on the left by 3.) We get:
Oh thank heavens, this looks much better. You know the drill! (If not check out this post on solving inequalities: Inequalities Part 4). We need to get x alone on one side. Right now we have x on both sides, let’s get the x terms on one side.
Great! Now we need to get x alone. First we handle any numbers that are being added or subtracted to x. Since 5 is being added to x, we need to subtract 5 from both sides.
Next, we handle any numbers that are being multiplied or divided by x. Since the x is being multiplied by a 20, we need to divide both sides by 20.
We can reduce the fraction.
We have officially solved for x! Let’s sketch our own number line quickly. (If you need a refresher, check out my blog post on sketching number lines: Number Lines: a quick refresher.)
We sketch something like this:
Good job! Now, compare that to the number lines we have to choose from. Which one could it be?
Our number line covers all negative values (all values to the left of the 0), so right away we can cross out options A, B, D, and E. Wow, we only have one option left: option C. Let’s compare just to make sure that’s the right choice, as a way to check our work:
Yes, option C could represent the inequality. Well done!