# How to 1/4x + 2/9 - 14 = 100

• kyphysics
In summary, Mastermind said that 1/4 is a coefficent of x and that x is NOT in the denominator of the first fraction.
kyphysics

## Homework Statement

Solve equation for x above.

See title.

## The Attempt at a Solution

Step 1: add 14 to both sides

1/4x + 2/9 = 114

Step 2: This is where my memory is a bit fuzzy.

I know we can obtain like bases between 1/4x and 2/9, but that wouldn't seem super helpful, because they aren't like terms is that correct? I figured 1/4 and 2/9 would be like terms, but 1/4x and 2/9 aren't and cannot be combined.

If that's the case, then it seems I'd have to deal with each fraction in both terms separately and one-by-one.

I chose to "get rid" of the 2/9 fraction first by multiplying it by 9/1 (as well as ever other term on both sides by the same 9/1) and got:

9/4x + 2 = 1026

Step 3: Subtract 2 from both sides

9/4x = 1024

Step 4: Get rid of fraction by multiplying both sides by 4/1 and this yields:

9x = 4096

Step 5: Divide both sides by 9 to isolate the x and get:

x = 455.11111111...

Not 100% sure I did this correctly. And wondering also if there was a different or easier way?

You're main object is to get ##x## by itself. Regarding step #2, you can treat ##\frac{2}{9}## the same way you treated ##-14##. They are like terms, after all.

Is your equation $\frac{1}{4x}$ or $\frac{x}{4}$ ? If it's the former then you have done it incorrectly

Mastermind01 said:
Is your equation $\frac{1}{4x}$ or $\frac{x}{4}$ ? If it's the former then you have done it incorrectly
I believe that he was implying the former.

ProfuselyQuarky said:
I believe that he was implying the former.

Then his last step his wrong , if he multiplies both sides by 4/1 he would get $\frac{9}{x} = 4096$ . Not the other way.

ProfuselyQuarky
Mastermind01 said:
Is your equation $\frac{1}{4x}$ or $\frac{x}{4}$ ? If it's the former then you have done it incorrectly

Hi, Mastermind

1/4 is a coefficent of x. Apologies, b/c I don't know how to use the symbols stuff here yet. So, the x is NOT in the denominator of the first fraction.

kyphysics said:
Hi, Mastermind

1/4 is a coefficent of x. Apologies, b/c I don't know how to use the symbols stuff here yet. So, the x is NOT in the denominator of the first fraction.
In that case, I believe that you're correct.

Mastermind01
kyphysics said:
Hi, Mastermind

1/4 is a coefficent of x. Apologies, b/c I don't know how to use the symbols stuff here yet. So, the x is NOT in the denominator of the first fraction.

Right. You have done it correctly then.

P.S : Here's a guide to Latex which implements the math symbols here: https://www.physicsforums.com/threads/introducing-latex-math-typesetting.8997/ This will help avoid future confusion.

Mastermind01 said:
Right. You have done it correctly then.

P.S : Here's a guide to Latex which implements the math symbols here: https://www.physicsforums.com/threads/introducing-latex-math-typesetting.8997/ This will help avoid future confusion.

Oh, good to know I'm correct. Very rusty with certain topics that I'm trying to plug leaks in this summer.

I am aware of LaTex, but haven't had time to really delve into learning it yet. I want to do so this summer though! I believe it will help me tremendously next year.

Mastermind01
kyphysics said:
Oh, good to know I'm correct. Very rusty with certain topics that I'm trying to plug leaks in this summer.

I am aware of LaTex, but haven't had time to really delve into learning it yet. I want to do so this summer though! I believe it will help me tremendously next year.

Good luck then!

Mastermind01 said:
Then his last step his wrong , if he multiplies both sides by 4/1 he would get $\frac{9}{x} = 4096$ . Not the other way.

Wait!

Did you mean my last step was wrong even IF I meant 1/4 as the coefficient of x, instead of x being in the denominator?

The two options you presented earlier weren't what I had meant. So just double checking one last time! Thanks again!

kyphysics said:
Wait!

Did you mean my last step was wrong even IF I meant 1/4 as the coefficient of x, instead of x being in the denominator?

The two options you presented earlier weren't what I had meant. So just double checking one last time! Thanks again!

No worries. Your last step is wrong only if x is in the denominator. Else it's correct.

gotcha, thx

kyphysics said:
Hi, Mastermind

1/4 is a coefficent of x. Apologies, b/c I don't know how to use the symbols stuff here yet. So, the x is NOT in the denominator of the first fraction.
Then use parentheses to remove all doubt.

What you wrote, 1/4x , literally means (1/4)x and is what you intended. However, if you include the parentheses, you remove all doubt regarding what you intended.

ProfuselyQuarky

## 1. What is the first step in solving "1/4x + 2/9 - 14 = 100"?

The first step is to simplify the equation by finding a common denominator for 1/4 and 2/9. In this case, the common denominator is 36. So the equation becomes 9/36x + 8/36 - 14 = 100.

## 2. How do you isolate the variable in "1/4x + 2/9 - 14 = 100"?

To isolate the variable, you need to get rid of all the other terms on the same side of the equation. In this case, you can start by subtracting 8/36 from both sides, which gives you 9/36x - 14 = 92. Then, you can add 14 to both sides, which gives you 9/36x = 106. Finally, you can multiply both sides by 36 to get rid of the fraction, giving you x = 954.

## 3. Can the equation "1/4x + 2/9 - 14 = 100" be solved without a calculator?

Yes, it can be solved without a calculator. You can use mental math or paper and pencil to simplify the equation and solve for x.

## 4. Is there more than one possible solution for "1/4x + 2/9 - 14 = 100"?

No, there is only one possible solution for this equation. Once you have simplified the equation and isolated the variable, there is only one value for x that will make the equation true.

## 5. Can you check your answer for "1/4x + 2/9 - 14 = 100"?

Yes, you can plug your answer back into the original equation to check if it is correct. In this case, plugging in x = 954 gives you 1/4(954) + 2/9 - 14 = 100, which simplifies to 238.5 + 8/9 - 14 = 100. After finding a common denominator and simplifying, you will see that the equation is true, confirming that x = 954 is the correct solution.

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