Can Someone Show Me How To Solve This 3/4x-5=2/3?

4 Answers

Winter Profile
Winter answered
Its quite simple, well to me because I've already done it, but lets get back to the lesson.

Intro: The process I will be performing is called inverse operating, which is pretty much meaning the opposite. The inverse operation of adding would be subtracting and the inverse of multiplication would be dividing.

Step 1: I don't want to tell you the answer so I constructed a new problem similar to the one you have.

1/4n-4=3/4

You would first start with the easiest, subtracting and adding. You would add 4 to 4 instead of subtracting it. This means that the 4 will become 0 leaving 1/4n in its place.

Step 2: Being familiar with fractions and their decimal values would be good to know in this situation. 1/4 in its decimal form is .25 and 3/4 in its decimal form is .75

After I complete step one this is how the problem will look:

1/4n=3/4
It will be easier to work with decimals so I would change the fraction into decimal which would look like this:

.25n=.75

Step 3: After completing step one and step 2 (step two is optional if you are good with fractions and decimals) then you must use the inverse operation procedure with the following. Instead of multiplying .25 to n you would divide .25n by .25n or .25m/.25n. Whatever you do to that side you must do to the other side, so divide .75 by .25 which will equal 3. After you follow step three the problem will look like this:

.25n/.25n=.75/.25
______
n=3

To check your answer you should substitute the variable with the answer to the problem like so:

1/4n-4=3/4

------> 1/4(3)=3/4 which is absolutely true! Good luck!!!!

thanked the writer.
Oddman
Oddman commented
Your original problem had (1/4)n - 4 = 3/4. The correct answer to this is n=19. 19/4 - 4 = 3/4.
Your mistake was in adding 4 to only one side of the equation, which made the second equation different from the first.
Oddman Profile
Oddman answered
Given (3/4)x - 5 = (2/3)

Find x

Solution
(3/4)x - 5 = (2/3)
(3/4)x = 5 2/3 (add 5 to both sides)
x = (5 2/3)/(3/4)

Now we have to simplify this a bit. First, we express 5 2/3 as an improper fraction. Then we invert 3/4 and multiply.
x = (5 2/3)/(3/4) = (17/3)/(3/4) = (17/3)*(4/3) = (17*4)/(3*3)
x = 68/9 = 7 5/9

Check
(3/4)(7 5/9) - 5 = (2/3)
(3/4)(68/9) - 5 = 2/3 (=(3/9)(68/4) - 5 = (1/3)(17/1) - 5)
17/3 - 5 = 2/3
17/3 - 15/3 = 2/3 (yes)

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