Post your question in the Comment section below, and we’ll answer it as fast as humanly possible.

- Video Course
- Video Course Overview - READ FIRST
- General GRE Info and Strategies - 7 videos (all free)
- Quantitative Comparison - 7 videos (all free)
- Arithmetic - 42 videos (some free)
- Powers and Roots - 43 videos (some free)
- Algebra and Equation Solving - 78 videos (some free)
- Word Problems - 54 videos (some free)
- Geometry - 48 videos (some free)
- Integer Properties - 34 videos (some free)
- Statistics - 28 videos (some free)
- Counting - 27 videos (some free)
- Probability - 25 videos (some free)
- Data Interpretation - 24 videos (some free)
- Analytical Writing - 9 videos (all free)
- Sentence Equivalence - 39 videos (all free)
- Text Completion - 51 videos (some free)
- Reading Comprehension - 16 videos (some free)

- Study Guide
- Office Hours
- Extras
- Guarantees
- Prices

## Comment on

Equation with Many Fractions## The last example is wrong, as

## Can you show your

Can you show your calculations?

Once we get to -5 = 8x, we divide both sides by 8 to get: -5/8 = 8x/8

Simplify to get: -5/8 = x

## Why can you multiply both

## Yes, it's okay to do that.

Yes, it's okay to do that.

When we do this, the only thing we need to be sure of is that x does not equal zero.

We can be certain that x does not equal zero, since the original equation wouldn't make any sense if x equaled zero.

## Why did you choose to

## Hi Garrett,

Hi Garrett,

In order to eliminate all fractions, we must multiply both sides of the equation by the least common multiple of all of the denominators (2x, 5 and 4x).

For more on this see: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

So, 20x is the least common multiple of 2x, 5 and 4x

Notice what happens if we just multiply both sides by 20.

We get: 20(1/2x + 3/5) = 20(1 + 3/4x)

Expand: 20/2x + 60/5 = 20 + 60/4x

Simplify: 10/x + 12 = 20 + 15/x

As you can see, we still have some fractions because we were unable to cancel out the x's in the denominators.

If we want to eliminate the existing fractions, we must multiply both sides by x.

We get: x(10/x + 12) = x(20 + 15/x)

Expand: 10x/x + 12x = 20x + 15x/x

Simplify: 10 + 12x = 20x + 15

etc.

So, rather than multiply both sides of the equation first by 20 and then later by x, we could have saved a step by multiplying both sides by 20x.

Does that help?

Cheers,

Brent

## I don't understand how you

## Let's take it step-by-step.

Let's take it step-by-step. When it comes time to multiple both sides by 20x (aka 20x/1), we'll show an extra step.

Given: 1/2x + 3/5 = 1 + 3/4x

Multiple both sides by 20x/1 to get: 20x/2x + 60x/5 = 20x + 60x/4x

Simplify: 10 + 12x = 20x + 15

Subtract 10 from both sides: 12x = 20x + 5

Subtract 20X from both sides: -8x = 5

Divide both sides by -8: x = -5/8

Does that help?

## Yes, thanks!

## my confusion is dropping the

## Let's use a nice fraction

Let's use a nice fraction property that says ab/cd = (a/c)(b/d)

So, we can write: 20x/2x = (20/2)(x/x)

= (10)(1)

= 10

Aside: We also used the fact that x/x = 1

## and the 60x/4x. why not 15x.

## We'll use the same fraction

We'll use the same fraction property: ab/cd = (a/c)(b/d)

So, we can write: 60x/4x = (60/4)(x/x)

= (15)(1)

= 15

Another way to verify whether 60x/4x = 15 is to TEST some values of x.

Try x = 2

60x/4x = 60(2)/4(2) = 120/8 = 15 PERFECT!

Try x = 3

60x/4x = 60(3)/4(3) = 180/12 = 15 PERFECT!

Try x = 10

60x/4x = 60(10)/4(10) = 600/40 = 15 PERFECT!

Since you are suggesting that 60x/4x = 15x, let's test this out by testing some more values

Try x = 2

Does 60x/4x = 15x?

Plug in x = 2 to get: 60(2)/4(2) = 15(2)

Evaluate both sides to get: 15 = 30

Doesn't work. So, it is not the case that 60x/4x = 15x

Does that help?

## That helps. Thanks

## When I added 1/2x + 3/5 I got

## Great question! First off,

Great question! First off, your solution strategy is perfectly valid (although perhaps longer).

We get x = 0 as a solution due to the fact that, if x = 0, the fractions on each side are UNDEFINED (since we're dividing by 0). The equation you created "behaves" as though x = 0 is a solution, but we must recognize that it's actually an invalid solution.

## I went at this in a

## Perfect!!

Perfect!!

## Hi, I did my math the same as

## In the future, it would help

In the future, it would help if you showed all of your calculations. Otherwise, I'm forced to guess the steps you took to get x = -8/5.

Here's my best guess at what you did.

Take: 1/2x + 3/5 = 1 + 3/4x

Rewrite first term as: 2/4x + 3/5 = 1 + 3/4x

Subtract 3/4x from both sides: -1/4x + 3/5 = 1

Subtract 3/5 from both sides: -1/4x = -2/5

Multiply from both sides by -4 to get: 1/x = -8/5

At this point, we know that 1/x = -8/5, however we want to find the value of x (not 1/x)

Take: 1/x = -8/5

Invert both sides to get: x/1 = -5/8

In other words, x = -5/8

Is that what happened in your solution?

Cheers,

Brent

## Hello, you said in a previous

## Hi Julian,

Hi Julian,

That's not quite what I said.

In Quantitative Comparison questions, you cannot multiply/divide the TWO QUANTITIES (Quantity A and Quantity B) by variables unless we are 100% sure that the variable is positive..

In this question, we are multiplying the given EQUATION by 20x. This is okay.

Here's the video that says you cannot multiply/divide the TWO QUANTITIES by variables unless we're sure the variable is positive: https://www.greenlighttestprep.com/module/gre-quantitative-comparison/vi...

Here's the video on solving EQUATIONS through matching operations: https://www.greenlighttestprep.com/module/gre-algebra-and-equation-solvi...

Does that help?

Cheers,

Brent

## Add a comment