BioHazard9064
  • BioHazard9064
Please help Im stuck on the last one. Solve for x: 2 over 5 (x - 4) = 2x.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{2}{5}(x-4) = 2x\]
anonymous
  • anonymous
Step : 1 - Multiply by 5 both the sides first.. Step : 2 - Then divide by 2 both the sides.. Step : 3 - Then, subtract \(x\) from both the sides. Step : 4 - Then, divide by 4 both the sides. Finally, you will get the value of \(x\)..
BioHazard9064
  • BioHazard9064
so multiply 2 over 5 by 5

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BioHazard9064
  • BioHazard9064
and 2x?
anonymous
  • anonymous
yes.. What you got after step 1?
BioHazard9064
  • BioHazard9064
10 over 5
anonymous
  • anonymous
Just do it, if you are wrong, I will correct, now try, don't hesitate..
anonymous
  • anonymous
Can't you cancel 5 with 5 there?
BioHazard9064
  • BioHazard9064
yes
BioHazard9064
  • BioHazard9064
oh the 5 cancels that 5 leaving me with 2
anonymous
  • anonymous
\[\frac{2}{5}(x-4) \times 5 = 2x \times 5 \\ \frac{2}{\cancel{5}}(x-4) \times \cancel{5} = 10x \\ 2(x-4) = 10x\]
anonymous
  • anonymous
This is what you get after step 1.. Now what you get after step 2??
BioHazard9064
  • BioHazard9064
then I divide by 2
anonymous
  • anonymous
yeah do it..
BioHazard9064
  • BioHazard9064
(x-4)=5x
anonymous
  • anonymous
Wow, superb..!! :) Now (x-4) you can write it as : x - 4, without brackets too, no harm...
anonymous
  • anonymous
\(x - 4 = 5x\)
anonymous
  • anonymous
Now, subtract \(x\) from both sides which is our 3rd step. Do it..
BioHazard9064
  • BioHazard9064
-4=5
anonymous
  • anonymous
LHS is -4.. that is only good, what about RHS?
anonymous
  • anonymous
\[x - 4 \color{red}{- x} = 5x \color{red}{-x} \\ \cancel{x} - 4 \color{red}{\cancel{-x}} = 5x \color{red}{- x} \\ -4 = 5x \color{red}{- x}\]
anonymous
  • anonymous
Now tell me what is \(5x-x\) = ??
BioHazard9064
  • BioHazard9064
5
anonymous
  • anonymous
How?
anonymous
  • anonymous
I tell you by one more method.. Okay, take \(x =2\), now \(5x = 5 \times 2 = 10\)
anonymous
  • anonymous
Is this good? I have taken the value of x = 2, x is any number there, it is variable, it can take any value, so I took its value as 2 just as an example...
anonymous
  • anonymous
\(5x\) means \(5 \times x\) that is 5 is multiplied with \(x\)..
BioHazard9064
  • BioHazard9064
sorry my computer froze and reset
BioHazard9064
  • BioHazard9064
so it pasted my last message
anonymous
  • anonymous
If I take x = 2, then \(5x\) becomes \(5 \times x = 5 \times 2 = 10\), this you got?
BioHazard9064
  • BioHazard9064
yes
anonymous
  • anonymous
So, you have : |dw:1437505195878:dw|
anonymous
  • anonymous
You are getting how I got \(5x-x\) = 4x ??
BioHazard9064
  • BioHazard9064
yes
anonymous
  • anonymous
Or you can do it by distributive property too.. \[5x - x\] Take \(x\) common from both: \[5x - x \\ 5x - 1x\\x(5-1) \\ x (4) \\ 4x\]
anonymous
  • anonymous
See, if have \(x-x\), then you will cancel that, if you have \(2x-2x\), then also you can cancel, both the terms should be same.. But here one is 5x and other is simply x, so it is quite risky to cancel it and get 0 marks for your answer..
anonymous
  • anonymous
So are you clear how we got 4x ?
BioHazard9064
  • BioHazard9064
Yes
anonymous
  • anonymous
Coming back to our original question: We reached: \[-4 = 5x - x \\ -4 = 4x\] This is what we got after step 3. Now do step 4..
BioHazard9064
  • BioHazard9064
1
anonymous
  • anonymous
Do it properly, what you got on Left Side?
BioHazard9064
  • BioHazard9064
-1
anonymous
  • anonymous
And on right side??
BioHazard9064
  • BioHazard9064
1
anonymous
  • anonymous
See, an equation has two sides and = sign in between, so write them fully when you are writing: So after 4th step you get: \[-1 = 1x \\ -1 = x \\ .. \\ \color{green}{x = -1}\]
anonymous
  • anonymous
Don't forget the x you are having on right side, why are you not considering x there?
BioHazard9064
  • BioHazard9064
I did
BioHazard9064
  • BioHazard9064
Would the answer be -1
anonymous
  • anonymous
\[-4 = 4x \\ \text{Divide by 4 :} \\ \frac{-\cancel4}{\color{red}{\cancel{4}}} = \frac{\cancel{4}x}{\color{red}{\cancel{4}}} \\ -1 = x\]
anonymous
  • anonymous
The value of \(x\) is \(-1\)..
BioHazard9064
  • BioHazard9064
Thank you for helping me to understand and not just giving me the answer
anonymous
  • anonymous
It is okay buddy, we are here to learn and get learned... :)
BioHazard9064
  • BioHazard9064
true

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