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## 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.

## 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!!

## 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

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