$6-3x<12\quad:\quad\begin{bmatrix}\mathrm{Solution:}\:&\:x>-2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-2,\:\infty\:\right)\end{bmatrix}$6−3x<12 : [ Solution: x>−2 Interval Notation: (−2, ∞ ) ]
Steps
$6-3x<12$6−3x<12
$\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}$Subtract 6 from both sides
$6-3x-6<12-6$6−3x−6<12−6
$\mathrm{Simplify}$Simplify
$-3x<6$−3x<6
$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$Multiply both sides by −1 (reverse the inequality)
$\left(-3x\right)\left(-1\right)>6\left(-1\right)$(−3x)(−1)>6(−1)
$\mathrm{Simplify}$Simplify
$3x>-6$3x>−6
$\mathrm{Divide\:both\:sides\:by\:}3$Divide both sides by 3
