Question

Find the solution set of the given inequality 6 - 4x ≥ 2x - 12 , x ∈ N and represent the solution graphically.​

Answer 1

Answer:

$6-4x\ge \:2x-12\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}$

Step-by-step explanation:

$6-4x\ge \:2x-12$

$\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}$

$6-4x-6\ge \:2x-12-6$

$-4x\ge \:2x-18$

$\mathrm{Subtract\:}2x\mathrm{\:from\:both\:sides}$

$-4x-2x\ge \:2x-18-2x$

$-6x\ge \:-18$

$\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}$

$\left(-6x\right)\left(-1\right)\le \left(-18\right)\left(-1\right)$

$6x\le \:18$

$\mathrm{Divide\:both\:sides\:by\:}6$

$\frac{6x}{6}\le \frac{18}{6}$

$x\le \:3$