Solving equations with fractions

[harmsway]

I'm learning to solve equations that involve fractions and requires use of both the addition principle and the multiplication principle without clearing fractions. I thought I had the formula down, until I reached problems with negatives in them.I have no idea what I am doing wrong and I've tried two different things, but I end up with the wrong answers. Is there a different formula I should be using?

Here's the problem:

-4 = 2/3x - 7

So I have to find out what x is (My answer book says it's 9/2) . And here's the two different ways I've tried, because after getting one wrong answer, I wasn't sure which number I was supposed to subtract (now, I don't even know if I'm supposed to subtract.)::


a) -4 - 2/3 = 2/3x - 7 - 2/3

-14/3 = - 7

1/7 * 14/3 = 7 * 1/7

2/3=x...

Obviously that is not the right answer.

In my second attempt:

b) -4 - 7 = 2/3x - 7 - 7

-11 = 40/3

3/40 * 11/1 = 40/3 * 3/40

33/40=x... yet again, far from the right answer.

I'm doing the formula the book shows.... Am I supposed to be doing it a different way? I've tried and tried, and I've tried the similar problems with the negative,and I just keep getting it wrong.

 

[Loren]

I hate to be the bearer of sad tidings, but you are doing a couple of things wrong, and maybe more. Let me say that it is usually better to multiply both sides of the equation by the least common denominator to "clear" fractions, but if your teacher said not to do this for this exercise. I guess we are stuck with doing it the hard way which will provide you with some practice in handling fractions.


a) -4 - 2/3 = 2/3x - 7 - 2/3

-14/3 = - 7 >>>When you subtract 2/3 from both sides you must remember that you can combine only "like" terms. A term containing a variable is different than a "plain ole number" term and they cannot be combined. Therefore this line should read "-14/3=2/3x-23/3".

1/7 * 14/3 = 7 * 1/7 <<<There is no x in this equation. I don't see how the next line can suddently have an x in it.

2/3=x...

b) -4 - 7 = 2/3x - 7 - 7 << This is good.

-11 = 40/3 <<<You can combine the two "-7"s but 2/3x cannot be combined with any term that does not contain an x. No other terms in this equation contain an x. Therefore this line must have the 2/3x still in it. This line should read "-11=2/3x".

3/40 * 11/1 = 40/3 * 3/40 <<Where is your x? You cannot throw it away and then arbitrarily have it reappear in the next line.

33/40=x
Now, you might be ready to try again.

 

[Denis]

I thought I had the formula down, until I reached problems with negatives in them.
Here's the problem:
-4 = 2/3x - 7
-4 - 2/3 = 2/3x - 7 - 2/3

That indicates you did NOT "have the formula down"...

Keep it simple; add 7 to each side:
-4 + 7 = 2/3x - 7 + 7
2/3x = 3

 

[masters]

I thought I had the formula down, until I reached problems with negatives in them.
Here's the problem:
-4 = 2/3x - 7
-4 - 2/3 = 2/3x - 7 - 2/3

That indicates you did NOT "have the formula down"...

Keep it simple; add 7 to each side:
-4 + 7 = 2/3x - 7 + 7
2/3x = 3

Now, multiply both sides by the reciprocal of \(\displaystyle \frac{2}{3} \ which \ is \frac{3}{2}\)

\(\displaystyle \frac{3}{2}\cdot\frac{2}{3}x = \frac{3}{2}\cdot3\)

\(\displaystyle x=\frac{9}{2}\)

 

[Denis]

2x/3 = 3
easier to crisscross multiply:
2x = 9
x = 9/2