How do I solve 3x + 6 = 9?

1 Answer
Nov 11, 2015

x=1

Explanation:

First of all I will use the shortcuts. After that I will show what is actually happening. This will help in all sorts of ways.

color(blue)("Short cut method")

Move the 6 to the other side of the = and change its sign giving:

3x =9-6
3x=3

Move the three to other side of the = sign
Because it is multiply on the left it becomes divide on the right

x= 3 divide 3
x=1

color(blue)("Now the explanation")
The best way is to explain it as I go along

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color(brown)("Step 1.")
Get just the x-terms on the left. In this case there is only 1
and that is 3x.

Subtract 6 from both sides

(3x+6 ) -6 = (9) -6

but +6 and -6 is 0 giving

3x+0 =9-6

but 9-6 is 3 giving

3x=3

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color(brown)("Step 2.")
Now lets get rid of the 3 in 3x
Note that 3x is in fact 3 times x

Divide both sides by 3 giving

(3 times x) divide 3 = (3) divide 3

But divide 3 is the same as times 1/3

(3 times x) times 1/3 = (3) times 1/3

3/3 times x = 3/3

but 3/3 is 1 giving

1 times x = 1
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1 times anything is itself so 1 times x is x

color(blue)("And we have our answer of "x=1)