Question

Find the values of w, 2 (w + 1) ≤ 4 (w + 2)
And plot it on a graph

Answer 1

Answer:

$2\left(w+1\right)\le \:4\left(w+2\right)\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:w\ge \:-3\:\\ \:\mathrm{Interval\:Notation:}&\:[-3,\:\infty \:)\end{bmatrix}$

Step-by-step explanation:

$2\left(w+1\right)\le \:4\left(w+2\right)$

$\gray{\mathrm{Expand\:}2\left(w+1\right):\quad 2w+2}$

$\gray{\mathrm{Expand\:}4\left(w+2\right):\quad 4w+8}$

$2w+2\le \:4w+8$

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

$2w+2-2\le \:4w+8-2$

$\gray{\mathrm{Simplify}}$

$2w\le \:4w+6$

$\gray{\mathrm{Subtract\:}4w\mathrm{\:from\:both\:sides}}$

$2w-4w\le \:4w+6-4w$

$\gray{\mathrm{Simplify}}$

$-2w\le \:6$

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

$\left(-2w\right)\left(-1\right)\ge \:6\left(-1\right)$

$\gray{\mathrm{Simplify}}$

$2w\ge \:-6$

$\gray{\mathrm{Divide\:both\:sides\:by\:}2}$

$\dfrac{2w}{2}\ge \dfrac{-6}{2}$

$\gray{\mathrm{Simplify}}$

$w\ge \:-3$