Question #de185

1 Answer
Apr 8, 2016

Answer:

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