Question

Which inequality below satisfies the solution set graphed on the following number line?432161 2 3 4 5 6OA.Z²-126OB.-3z²+3z +18 20OC.-2² +62-zOD. 32²-32-18 ≤0

Answer 1

Explanation

We are given the following number line:

We are required to determine the inequality that satisfies the number line given.

We know that the number line translates thus:

$x\leq-2\text{ }or\text{ }x\ge3$

We also know that the general rule for quadratic inequalities states:

We can achieve the inequality by solving for each option given as follows:

- Option A:

$\begin{gathered} x^2-x\ge6 \\ x^2-x-6\geqslant0 \\ \text{ Suppose }x^2-x-6=0 \\ x^2-3x+2x-6=0 \\ (x^2-3x)(+2x-6)=0 \\ x(x-3)+2(x-3)=0 \\ (x+2)(x-3)=0 \\ x=-2\text{ }or\text{ }x=3 \\ hence,\text{ the answer becomes:} \\ x\leq-2;x\ge3 \end{gathered}$

Hence, the answer is:

$x^{2}-x\geqslant6$

Option A is correct.