Answer
The solution is $(-\infty,1]\cup[3,\infty)$
Work Step by Step
$|12-6x|+3\ge9$
Take $3$ to the right side of the inequality:
$|12-6x|\ge9-3$
$|12-6x|\ge6$
Solving this absolute value inequality is equivalent to solving two separate inequalities, which are:
$12-6x\ge6$ and $12-6x\le-6$
$\textbf{Solve the first inequality:}$
$12-6x\ge6$
Take $12$ to the right side:
$-6x\ge6-12$
$-6x\ge-6$
Take $-6$ to divide the right side and reverse the direction of the inequality sign:
$x\le\dfrac{-6}{-6}$
$x\le1$
$\textbf{Solve the second inequality:}$
$12-6x\le-6$
Take $12$ to the right side:
$-6x\le-6-12$
$-6x\le-18$
Take $-6$ to divide the right side and reverse the direction of the inequality sign:
$x\ge\dfrac{-18}{-6}$
$x\ge3$
Expressing the solution in interval notation:
$(-\infty,1]\cup[3,\infty)$
