Finding for a Single Variable

[mstcrow5429]

If I'm finding X, and I have -1/2x + 3 = 1, I multiply each side by 2/1. However, if I have 1/2x + 3 = 1, I multiply each side by 2/1, not -2/1, correct? I think I'm missing a basic connection here. Thanks.

[DixieGirl]

If I'm finding X, and I have -1/2x + 3 = 1, I multiply each side by 2/1. However, if I have 1/2x + 3 = 1, I multiply each side by 2/1, not -2/1, correct? I think I'm missing a basic connection here. Thanks.

1/2x + 3 = 1
2/1(1/2x + 3 = 1 )
X + 6 = 2
X = -4

-1/2x + 3 = 1
2/1(-1/2x + 3 = 1 )
-X + 6 = 2
-X = -4
X = 4

[Drummerboy]

If I'm finding X, and I have -1/2x + 3 = 1, I multiply each side by 2/1. However, if I have 1/2x + 3 = 1, I multiply each side by 2/1, not -2/1, correct? I think I'm missing a basic connection here. Thanks.

Remember that whatever you multiply to one side of the equation, you must multiply to the other. In other words, you can multiply -2/1 or 2/1 to both problems as long as you do the same to the other side of the equation. DixieGirl showed you one way, so let's try it the other way:

1/2x + 3 = 1

Multiply -2/1 to both sides (-2/1)(1/2x +3) = (-2/1)1
Negative signs on both sides -x - 6 = -2
Add +6 to both sides -x= 4
Multiply -1 to both sides to cancel negative on "x" (-1)(-x) = (-1)(4)
This equals x = -4 Answ.


Try this one:


-1/2x + 3 = 1

Multiply -2/1 to both sides (-2/1)(-1/2x + 3) = (-2/1)1
Negative signs cancel on left side x - 6 = -2
Add +6 to both sides x = 4 Answ.


These are the same answers DixieGirl came to. The only difference is that I multiplied by a negative 2/1 instead of a positive 2/1. As long as you do the same thing to both sides, it doesn't matter which number you use, mathematically.


Food for thought:

Problem: -1/2x + 3 = 1

Multiply both sides by 6: 6(-1/2x + 3) = 6(1)
Equals -3x + 18 = 6

Now, add -18 to both sides: -3x = -12
Divide both sides by -3: x=4, Answ.

The answer is still 4, even though at the beginning you multiplied both sides by 6!

Hope this helps!

[mstcrow5429]

K, how do you do 2/3 (7/8 - 4x) - 5/8 = 3/8

I get -21/50, but the given answer is -5/32. Thanks.

[Drummerboy]

Okay, first you want to multiply the 2/3 to the numbers in parenthesis. 2/3 is part of the left side of the equation, so it only is multiplied by those numbers in the parenthesis. This gives:

7/12 - 8/3x - 5/8 = 3/8

Now, add 7/12 to -5/8, which gives:-8/3x - 1/24 = 3/8
Add +1/24 to both sides, which gives: -8/3x = 5/12
Divide both sides by -8/3: x = -5/32, Answ.

Hope this helps!

[mstcrow5429]

Okay, first you want to multiply the 2/3 to the numbers in parenthesis. 2/3 is part of the left side of the equation, so it only is multiplied by those numbers in the parenthesis. This gives:

7/12 - 8/3x - 5/8 = 3/8

Now, add 7/12 to -5/8, which gives:-8/3x - 1/24 = 3/8
Add +1/24 to both sides, which gives: -8/3x = 5/12
Divide both sides by -8/3: x = -5/32, Answ.

Hope this helps!

K, I get to 7/12 - 8/3x - 5/8 = 3/8, then I think I need a common denominator to subtract. So use 24 as the lowest common denominator, which results in:

14/24 - 64/24x - 15/24 = 9/24

Adding 15/24 to both sides:

14/24 - 64/24x = 24/24

Subtracting 14/24 from both sides:

-64/24x = 14/24

Then I'm not sure what to do.

[Drummerboy]

K, I get to 7/12 - 8/3x - 5/8 = 3/8, then I think I need a common denominator to subtract. So use 24 as the lowest common denominator, which results in:

14/24 - 64/24x - 15/24 = 9/24

Adding 15/24 to both sides:

14/24 - 64/24x = 24/24

Subtracting 14/24 from both sides:

-64/24x = 14/24

Then I'm not sure what to do.

First of all, you made a little mistake when you subtracted 14/24 from both sides. You would have 24/24 - 14/24 = 10/24 on the right side of the equation. Then, you would have:

-64/24x = 10/24

Next, divide both sides by -64/24 in order to get "x" by itself. You will have x = - 5/32, which is your answer.

BUT . . .

But you got too complicated with your equation. Although you can figure it the way you did because what you did to one side of the equation you did to the other, you want to do the problem as simply as possible. First, make sure all your terms are added together on one side of the equation if they can be. In this case, add 7/12 to -5/8. You will only need to convert these to common denominators instead of converting all your terms to common denominators. 7/12 converts to 14/24 and -5/8 becomes -15/24.

14/24 - 15/24 = -1/24. So now you have:

-8/3x - 1/24 = 3/8 (Both sides are simplified).

Then, add +1/24 to both sides. You will have to find a common denominator again. 3/8 becomes 9/24. So, 1/24 + 9/24 = 10/24. The equation is now:

-8/3x = 10/24

Divide both sides by -8/3 to isolate "x". You have x = -5/32, Answ.



You see, we did not have to convert all the terms to a common denominator because all the terms still are in the same proportion. In other words:

Say you have 1/2 + 1/4. You need to add them together. You can make 1/2 become 2/4.

1/4 + 2/4 = 3/4

Now, you could have also coverted 1/2 to 10/20, but it still was 1/2. Remember anything multiplied by 1 is itself? That is exactly what you did---multiplied 1/2 by 1 to get a common denominator, although it was a fraction like 2/2.

1/2 x 2/2 (which is really another way of saying 1) = 2/4 (which is another way of saying 1/2).


Does this make sense? You might have to review a book like Cliff's QuickReview for Algebra. I used that book for preparing for the ACT and liked it a lot.

[stitches013]

I think this is it. I had to try this a few times. It was the 2/3 times 4x that threw me a couple times. I kept doing the same thing you are doing.

Please see below. Hope it helps...sheesh!

Original 2/3(7/8-4x)-5/8=3/8

1)Expand first set
=> ((2/3)(7/8)-(2/3)(4)x)-5/8=3/8

2)ADD 5/8 to both sides, cancelling the one on the left
=> ((14/24)-8/3(x))=8/8

3)SUBTRACT 14/24 from both sides, cancelling the one on the left
=> -8/3(x)=8/8-14/24

4)MULTIPLY BOTH SIDES BY "3"
=> -8x=24/8-42/24

5)THEN Divide BOTH SIDES BY "-8" OR MULTIPLY BY "-1/8"
=> x=((24/8)(-1/8))-((42/24)(-1/8))

6)Resulting in
=> x=(24/64)+(42/192)

7)Reduce Fractions using GCF (64)
=> x=-(24/64)+(14/64)

8)Add the Fractions
=> x=-10/64

9)Reduce Fraction
=> x=-5/32 (ANSWER!!!)


~Rich

[mstcrow5429]

K, I got it, I think. I hope this isn't going to be a large part of the CLEP College Algebra exam.

[DixieGirl]

This is one of the major building blocks of algebra. So, you may want to make sure that you know this really well.