# How do you solve 7x + 6= 3x + 9?

Sep 11, 2017

$\textcolor{b l u e}{x = \frac{3}{4}}$

#### Explanation:

In solving for $x$ (the unknown variable), the GOLDEN RULE OF ALGEBRA (COMBINING AND BALANCING THE EQUATION TO SOLVE FOR THE UNKNOWN). (Isolating the variable to get its unknown value)

Steps:
1. Isolate the unknown variable by moving it to the left side of the equation. (also eliminating the other variables to get the final format of color(blue)(x = ?), where $x$ is the unknown variable.
2. Combine like terms, balance the equation.
3. Simplify the answer to get the unknown value.

$7 x + 6 = 3 x + 9$

let's combine the like terms, $7 x \mathmr{and} 3 x$ then $6 \mathmr{and} 9$

remember the GOLDEN RULE, To balance the equation to get the unknown, to remove the $3 x$ on the RIGHT side of the equation, we must subtract $- 3 x$ on the RIGHT side, to balance it you must subract $3 x$ to the LEFT side of the equation.

$\textcolor{b l u e}{\left(- 3 x\right)}$ $7 x + 6 = 3 x + 9$ color(blue)((-3x)

$4 x + 6 = 9$

we need to isolate the LEFT side of the equation to get the x = ??? format, to get the unknown value, therefore, we must remove $+ 6$, always remember the GOLDEN RULE, (Balancing the Equation, To get the unknown value)

$\textcolor{b l u e}{\left(- 6\right)}$ $4 x + 6 = 9$ $\textcolor{b l u e}{\left(- 6\right)}$

$4 x = 3$

to, remove $4$ from $4 x$, we must divide it both sides of the equation by $4$.

$\frac{\cancel{4} x}{\cancel{4}} = \frac{3}{4}$

so the final answer is $\textcolor{b l u e}{x = \frac{3}{4}}$

the other way also like this is also correct,

$7 x + 6 = 3 x + 9$
$\textcolor{b l u e}{\left(- 6\right)}$ $7 x + 6 = 3 x + 9$ $\textcolor{b l u e}{\left(- 6\right)}$
$7 x = 3 x + 3$
$\textcolor{b l u e}{\left(- 3 x\right)}$ $7 x = 3 x$ + 3 $\textcolor{b l u e}{\left(- 3 x\right)}$
$4 x = 3$
$\frac{\cancel{\left(4\right) x}}{4} = \frac{3}{4}$

$\textcolor{b l u e}{x = \frac{3}{4}}$

also correct :)