# Solve for x – (x * 20/90) = 45

#### Rayl333

##### New member
Solve for x – (x * 20/90) = 45

Please solve for x – (x * 20/90) = 45

Help solving it step by step.

Believe it or not have done way more complex equations in the past involving 3D math with geodesic domes. Even emulated R Buckminster Fuller's design on struts for a dome using dihedral angles (tessellate or fit dome triangle panels to fit flush) and making domes with arches instead of struts (or straight lines). But this was a few years ago and somehow this simple equation is stumping me with where the x's are!

Also have a website called GeoArch Domes (nonprofit and educational)

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#### Dr.Peterson

##### Elite Member
Please solve for x – (x * 20/90) = 45

Help solving it step by step.
Start by simplifying the left side, by combining like terms.

#### JeffM

##### Elite Member

First, simplify each fraction.

Second, multiply both sides of the equation by the product of the denominators of the simplified fractions.

Life will then be easier.

#### tkhunny

##### Moderator
Staff member
Third, get past the mystical belief that fractions are scary or that equations with fractions are ANY different from other equations. Fractions are just numbers. No need to be afraid of them or to assign them any other level of difficulty.

#### mmm4444bot

##### Super Moderator
Staff member
… get past the mystical belief that fractions are scary … No need to be afraid of them …
Why did you post this?

#### Rayl333

##### New member
Thanks much to all! Your prompt replies are invaluable.

Not scared of fractions. Another thing that might throw me is getting Theta and Phi mixed up, and some math books (maybe older ones) do just that. But I love math!

#### JeffM

##### Elite Member
Thanks much to all! Your prompt replies are invaluable.

Not scared of fractions. Another thing that might throw me is getting Theta and Phi mixed up, and some math books (maybe older ones) do just that. But I love math!
theta = $$\displaystyle \theta$$

phi = $$\displaystyle \phi$$

You do not need to remember the names of the symbols, merely see the difference visually and be consistent in usage. If you want you call them oh-horizontal and oh-vertical, it makes no difference. The point is that each different visual symbol relates to a different unknown or variable. I never remember the name of zeta when I see it (I usually call $$\displaystyle \zeta$$ squiggle and have been known to mix up mu and nu. It makes no difference: I am dealing with visual symbols, not names of sounds. It would be different if I ever decided to become educated and learn Greek.

About fractions. I HALF-agree with tkhunny's point about fractions. CONCEPTUALLY, they are numbers like any other and present no differences in ALGEBRAIC principle to any other number. Yet they add special mechanical considerations that present additional opportunities for error. Those of us who are error prone have found that poor weak sublunary creatures such as we do better when we eliminate fractions early.

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#### Rayl333

##### New member
x - 2x/9 = 45
x(1 - 2/9) = 45
Continue...(we don't provide full solutions)

Edit: sorry Dr.P, didn't see your post...
Denis, one question - how did you get from x - 2x/9 = 45 to x(1 - 2/9) = 45. IOW derive 1 from 2x & put it in parenthesis?

#### Dr.Peterson

##### Elite Member
Another thing that might throw me is getting Theta and Phi mixed up, and some math books (maybe older ones) do just that.
Can you explain in what way math books get these letters mixed up? I presume you aren't talking about reading them incorrectly, but perhaps the fact that they are not always used in the same way.

For example, MathWorld shows how different sources swap them (or use different forms of them) for the two angles in spherical coordinates. Wikipedia indicates that the difference is between usage in physics and in math. In such situations, you just have to read carefully to see which convention your current book is following.

#### Rayl333

##### New member
Can you explain in what way math books get these letters mixed up? I presume you aren't talking about reading them incorrectly, but perhaps the fact that they are not always used in the same way.

For example, MathWorld shows how different sources swap them (or use different forms of them) for the two angles in spherical coordinates. Wikipedia indicates that the difference is between usage in physics and in math. In such situations, you just have to read carefully to see which convention your current book is following.
Agree. In my 2005 amazon.com review of the book Geodesic Math and How to Use It, to quote "One thing - spherical coordinate symbols for Theta & Phi are switched, though referenced in correct order (check Mathworld). Easy to correct, just read "Phi symbol" as Theta & "Theta symbol" as Phi - references & formulas will be in order. This book was written in mid-1970's, guess more? people then used this as convention."

#### mmm4444bot

##### Super Moderator
Staff member
Denis … how did you get from x - 2x/9 = 45 to x(1 - 2/9) = 45.
This is called factoring.

On the left-hand side of the equation, there are two terms: x and 2x/9. The second term is being subtracted from the first.

Each of these terms contains a factor of x, so x can be "pulled out" and placed in front of grouping symbols. What remains after factoring out the x from each term appears inside the grouping symbols.

Do you remember the Distributive Property? If not, I suggest you google it, and refresh your memory. It's very important to understand, when working with algebraic expressions:

a(b - c) = a·b - a·c

On the left-hand side, we see two quantities being multiplied. One quantity is a; the other is b-c. The Distributive Property tells us, when performing this multiplication, that each term inside the parentheses gets multiplied by the factor outside. The result is shown on the right-hand side.

Well, simple factoring is the reverse of distribution. In other words, we may read the equation above from right to left, too.

Note on the right-hand side that each term contains a factor of a. Therefore, we can factor out the a, by placing it in front of grouping symbols surrounding what remains. We say that the expression on the left-hand side is "factored"; the equivalent expression on the right-hand side is "expanded".

Google factoring linear binomials, to see more examples of the process. :cool:

#### mmm4444bot

##### Super Moderator
Staff member
I forgot to mention the following.

When factoring an expression like x - 2x/9, you need to remember that all numbers (symbolic or otherwise) can be viewed with a factor of 1 in front of them, if needed.

In other words, look at your expression like this: 1x - 2x/9. That's where the 1 comes from, in Denis' factored form.

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#### Rayl333

##### New member
For example, MathWorld shows how different sources swap them (or use different forms of them) for the two angles in spherical coordinates. Wikipedia indicates that the difference is between usage in physics and in math. In such situations, you just have to read carefully to see which convention your current book is following.
And apparently according to Neil deGrasse Tyson, many physicists rely on mathematicians for a lot of their answers!

#### mmm4444bot

##### Super Moderator
Staff member
And apparently according to Neil deGrasse Tyson, many physicists rely on mathematicians for a lot of their answers!
I would add that all physicists rely on mathematics for interpreting their "answers".

#### Subhotosh Khan

##### Super Moderator
Staff member
I would add that all physicists rely on mathematics for interpreting their "answers".
Yes ... Einstein did ..... Heissenberg did.... Engineers do it en masse....