Please explain this simple equation: 5=9 -2x

[AdultLearningMathAgain]

Hello Everyone!

The equation is a simple one but I don't understand the "why" of it.

$$5=9 -2x$$
The way I tried to solve it was I first targetted the "9" and did a -9 on both sides, but according to the book, I should have done a -2x instead.

When I see an equation like above, I usually target the "free number" first before going for the x, so I'm confused.

Thanks!

 

[blamocur]

I cannot comment on the book's suggestion, but what do you get when you use your approach ?

 

[AdultLearningMathAgain]

I cannot comment on the book's suggestion, but what do you get when you use your approach ?

x= -2

 

[Deleted member 4993]

Hello Everyone!

The equation is a simple one but I don't understand the "why" of it.

$$5=9 -2x$$
The way I tried to solve it was I first targetted the "9" and did a -9 on both sides, but according to the book, I should have done a -2x instead.

When I see an equation like above, I usually target the "free number" first before going for the x, so I'm confused.

Thanks!

Your method of eliminating '9' first is valid.

It is just two different ways to get to the same results.

 

[AdultLearningMathAgain]

At the end I get -4 divided by 2, which is -2, yes?

I am trying to write the equation here but it 's not working too good for me

 

[Deleted member 4993]

x= -2

That answer is incorrect. Can you please show your work?

 

[blamocur]

At the end I get -4 divided by 2, which is -2, yes?

I am trying to write the equation here but it 's not working too good for me

What happens when you substitute $x$ by -2 ? Do you get equal values on the left and the right hand side?

 

[BigBeachBanana]

At the end I get -4 divided by 2, which is -2, yes?

I am trying to write the equation here but it 's not working too good for me

$$5=9-2x\\ 5 + \blue{-9}=9-\blue{9} -2x \quad \text{subtract 9 on both sides}\\ \frac{-4}{\blue{2}}=\frac{-2x}{\blue{2}} \quad \text{ divide both sides by 2}\\ -2=\red{-}x$$This is what you arrived so far. Notice you have $-x$, not x. Need one more step to get the final answer.

 

[AdultLearningMathAgain]

$$5=9-2x\\ 5 + \blue{-9}=9-\blue{9} -2x \quad \text{subtract 9 on both sides}\\ \frac{-4}{\blue{2}}=\frac{-2x}{\blue{2}} \quad \text{ divide both sides by 2}\\ -2=-x$$This is what you arrived so far. Notice you have $-x$, not x. Need one more step to solve get the final answer.

I'm struggling to get the hang of writing the way you did, till then, here is a (crappy) picture that I hope will work.

 

[BigBeachBanana]

I'm struggling to get the hang of writing the way you did, till then, here is a (crappy) picture that I hope will work.

What do you get when you take -2 divided by 2?

 

[Harry_the_cat]

Notice that on the right hand side, when you cancel the 2s, you are left with -x not x.
That is you should have -2 = -x leading to x=2.
You have just ignored the -ve sign on the RHS.

 

[Steven G]

5 = 9 - 2x

I don' think that you should do things so mechanically.
2x is unknown, so call it what

Now 5 = 9 - 2x becomes 5 = 9 - what. I hope you see that the what becomes 4 (since 5 = 9 - 4)

So 2x=4. 2 times what equals 4---- 2x2 = 4
So x=2.

Just use common sense logic.