Question

Determine whether the ordered pair is a solution of the linear inequality.
x ≤ 3; (–2, 6)

Answer 1

`x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}`

Thus, -2 comes under the interval domain of the inequality (-∞, 3].

Hence, (-2, 6) is a solution to the linear inequality.

Explanation:

Given the linear inequality

x ≤ 3

substitute the value of x = -2

-2 ≤ 3

TRUE

It is clear that -2 is indeed less than 3. Thus, the ordered pair (-2, 6) is a solution to the linear inequality.

Also,

`x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}`

Thus, -2 comes under the interval domain of the inequality (-∞, 3].

Hence, (-2, 6) is a solution to the linear inequality.