Question

Question #de185

Answer 1

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.

Suppose we had:

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: `color(brown)(6+a+b=36)`

Suppose I was to `color(blue)("subtract "6" ")` from both sides of the equals sign.

`color(brown)(6color(blue)(-6)+a+b=36color(blue)(-6))`

On the left had side we have `color(brown)(6)color(blue)(-6)color(green)( =0)`
On the right hand side we have `color(brown)(36)color(blue)(-6)color(green)(=30)`

so `color(brown)(6color(blue)(-6)+a+b=36color(blue)(-6))` becomes `color(brown)(color(green)(0)+a+b=color(green)(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