Question

Solve, 2k + 3 ≤ 7k + 1

Answer 1

Answer:

2k + 3 ≤ 7k +1

2k -7k ≤ 1 - 3

-5k ≤ -2

k ≤ 2/5

Answer 2

Answer:

$2k+3\le \:7k+1\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:k\ge \dfrac{2}{5}\:\\ \:\mathrm{Decimal:}&\:k\ge \:0.4\\ \:\mathrm{Interval\:Notation:}&\:\left[\dfrac{2}{5},\:\infty \:\right)\end{bmatrix}$

Step-by-step explanation:

$2k+3\le \:7k+1$

$\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}$

$2k+3-3\le \:7k+1-3$

$\mathrm{Simplify}$

$2k\le \:7k-2$

$\mathrm{Subtract\:}7k\mathrm{\:from\:both\:sides}$

$2k-7k\le \:7k-2-7k$

$\mathrm{Simplify}$

$-5k\le \:-2$

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

$\left(-5k\right)\left(-1\right)\ge \left(-2\right)\left(-1\right)$

$\mathrm{Simplify}$

$5k\ge \:2$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\dfrac{5k}{5}\ge \dfrac{2}{5}$

$\mathrm{Simplify}$

$k\ge \dfrac{2}{5}$