Answer
$x$ = $-6$
Work Step by Step
Given equation is-
$\frac{1}{2}x-3$ = $6+2x$
Algebraic Solution:
Isolating $x$ on one side of the equation-
$2x-\frac{1}{2}x$ = $-3-6$
i.e. $\frac{3}{2}x$ = $-9$
i.e. $x$ = $\frac{-2\times9}{3}$ = $\frac{-18}{3}$
i.e. $x$ = $-6$ is the required solution
Graphical Solution:
On rearranging the given equation-
$2x-\frac{1}{2}x+3+6$ = $0$
i.e. $\frac{3}{2}x+9$ = $0$
Now graphing $y$ = $\frac{3}{2}x+9$
We see that graph intercept $x-axis$ at $-6$
Thus from the graph we conclude that the solution is $x$ = $-6$