# How do I solve 3x + 6 = 9?

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.

$\textcolor{b l u e}{\text{Short cut method}}$

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

$3 x = 9 - 6$
$3 x = 3$

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

$x = 3 \div i \mathrm{de} 3$
$x = 1$

$\textcolor{b l u e}{\text{Now the explanation}}$
The best way is to explain it as I go along

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Step 1.}}$
Get just the x-terms on the left. In this case there is only 1
and that is $3 x$.

Subtract 6 from both sides

$\left(3 x + 6\right) - 6 = \left(9\right) - 6$

but +6 and -6 is 0 giving

$3 x + 0 = 9 - 6$

but 9-6 is 3 giving

$3 x = 3$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b r o w n}{\text{Step 2.}}$
Now lets get rid of the 3 in $3 x$
Note that $3 x$ is in fact $3 \times x$

Divide both sides by 3 giving

$\left(3 \times x\right) \div i \mathrm{de} 3 = \left(3\right) \div i \mathrm{de} 3$

But $\div i \mathrm{de} 3$ is the same as $\times \frac{1}{3}$

$\left(3 \times x\right) \times \frac{1}{3} = \left(3\right) \times \frac{1}{3}$

$\frac{3}{3} \times x = \frac{3}{3}$

but $\frac{3}{3}$ is 1 giving

$1 \times x = 1$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1 times anything is itself so $1 \times x$ is $x$

$\textcolor{b l u e}{\text{And we have our answer of } x = 1}$