Solving for a variable

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Bollinger

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Feb 16, 2015
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I have the problem

t= 29 - ½(w - k) Solve for k

First I add the opposite of ½ and distribute, giving me

t = 29 + (-½w) + (½k)

then I multiply both sides by -2w because -2w is the reciprocal of -½w

t * -2w = 29 + (½k)

then I subtract 29 from both sides giving me

t * -2w + -29 = ½k

Then I multiply everything by 2 giving me

k = 2t * -4w + -58

Which according to this math software is wrong. It has been wrong before though, so I'm just checking to see where the fault lies and if it's on my end, which step I'm not getting.

Thanks.

Edit: Found and fixed and error where I was adding instead of multiplying. That might have been the issue, but I'm leaving this up just to see if I ultimately got it right.
 
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I suppose so, that gives me

k = 2t + w + -58

Which seems right. Still not sure what was invalid about my approach, though it obviously didn't result in the right answer. Multiplying everything by 2 was certainly the more sensible approach, not sure why I didn't catch that.
 
Bollinger said:
I suppose so, that gives me

k = 2t + w + -58

Which seems right. Still not sure what was invalid about my approach, though it obviously didn't result in the right answer. Multiplying everything by 2 was certainly the more sensible approach, not sure why I didn't catch that.
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Commenting on your original
Bollinger said:
I have the problem

t= 29 - ½(w - k) Solve for k

First I add the opposite of ½ and distribute, giving me

t = 29 + (-½w) + (½k) <==== maybe more grouping signs, i.e. + ((-½)w), would make it clearer

then I multiply both sides by -2w because -2w is the reciprocal of -½w

t * -2w = 29 + (½k) <====wrong should add (1/2) w to both sides, makes rest wrong
...
Click to expand...
 
Ok, I think I see what I did wrong. Is it okay to post another problem here, it's basically the same stuff so the subject still fits.

I have the problem

4x + 6y = 24 solve for y

First I divide both sides by 6 to get remove the coefficient from y

4x + y = 4

Then I divide both sides by 4 to do the same to x

x + y = 1

Then I add the opposite of x to both sides leaving me with

y = 1 + (-x)

Which is wrong. It tells me to check my answer by substituting in my value for y, but I don't really understand how to do that when my value has a variable. Any tips for that and of course for working out the mistake I made in the original problem.
 
You made the same mistake in both examples so let's go over it carefully.

You know that for examples 8+ 4 = 12

If for whatever reason you want to divide the 4 by 4 you can't say well I divide the left side by 4 so I must divide the right side by 4 and get 8 + 1 =3 which is not true.

Here is what happened: You really divided part of the left side by 4 and all of the right side by 4 so in the end the equal sign is not correct.

Here is a similar example to 4x + 6y = 24

3x + 9y = 27, solve for y.
step 1: identify the terms. They are 3x, 9y and 27
step 2: decide which term has a y in it. The y is in the 9y term.
step3: Get the 9y term alone on one side of the equation by moving the terms around. When you move a term across to the other side of the equal sign then the sign of that term changes. If you do not move the term across the equal sign, then the sign stays the same. To 9y alone we just move the +3x to the other side of the equal sign and get
9y = 27 -3x.
step 4: divide the left side by whatever the y is multiplied by. In this case y is being multiplied by 9.
If we divide the whole left side by 9 then we must divide the whole right side by 9. We get y = (27 - 3x)/9

One more example.

5x -3y = 11, solve for y

5x - 11 = 3y

y = (5x-11)/3
 
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