# How do I solve/write this word expression phrase: "A number added to the difference of 3 and five times the number"?

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To answer this question, we simply look at what the question is asking for.

We look for a few key words in order to figure out what this problem has.

**"Is" almost always means "="** You can almost always see "is" and "equals" as the same thing, but since we don't see those in this problem, we know we're dealing with an expression, not an equation.

Now, these are usually the terms I see most often that throw off students. They aren't so relevant in this problem, but I hope those help you in similar ones!

We know we have an expression. Whenever it says "a number" or "the number" or "that number," to me that means "x."

So, reading the question:

"A number" will be: `x`

We continue

"added to" will be: `+`

So, "a number added to" will be: `x+`

Now, moving on:

"the difference of" will be something subtrated by something else. What this tells us now, though, is that we'll have parentheses:

`x+ (...)`

Now we have : "3 and 5 times the number"

So, inside the parentheses will be 3 - 5*x:

`x+(3-5*x)`

And that's about it. I hope that helps some!

To solve:

"A number added to the difference of 3 and five times the number"

Let the number be x

*five times the number* = 5*x = **5x**

**Case 1.**

**difference of ***3* **and** *five times the number *= **3 - 5x **

*number added *

**to**

*the difference of 3 and five times the number*

= (3-5x) + x = 3 -5x - x = **3-4x**

**Case 2.**

But the difference can be taken by changing the sequnce so that

**difference of ***3* **and** *five times the number *= **5x - 3**

*number added *

**to**

*the difference of 3 and five times the number*

= (5x-3) + x = 5x - 3 - x = **6x-3**

There are two answers because the sequence for taking the difference is not specified