# Question #de185

Apr 8, 2016

See explanation

#### Explanation:

Algebra is exactly like manipulating numbers. The only difference is that you do not know the values of the numbers you are dealing with. You have to show that a number is there somehow so you use a letter in stead.

6 + "some number the value of which we do not know"

It is much simpler to write

$6 + a$

The thing is, we may have two numbers that we do not know the value of. So we could write:

$6 + a + b$

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You can not do much with $6 + a + b$ when it is on its own.

Instead, suppose we had: $\textcolor{b r o w n}{6 + a + b = 36}$

Suppose I was to $\textcolor{b l u e}{\text{subtract "6" }}$ from both sides of the equals sign.

$\textcolor{b r o w n}{6 \textcolor{b l u e}{- 6} + a + b = 36 \textcolor{b l u e}{- 6}}$

On the left had side we have $\textcolor{b r o w n}{6} \textcolor{b l u e}{- 6} \textcolor{g r e e n}{= 0}$
On the right hand side we have $\textcolor{b r o w n}{36} \textcolor{b l u e}{- 6} \textcolor{g r e e n}{= 30}$

so $\textcolor{b r o w n}{6 \textcolor{b l u e}{- 6} + a + b = 36 \textcolor{b l u e}{- 6}}$ becomes $\textcolor{b r o w n}{\textcolor{g r e e n}{0} + a + b = \textcolor{g r e e n}{30}}$

So now we know that $a + b = 30$. We still do not know their values but at least we know something about them!
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Suppose we had $x + 4 = 5$

Subtract 4 from both sides

$x + 4 - 4 = 5 - 4$

$x + 0 = 1$

$x = 1$

Hope this helps