Fluency exercise

## Problem

Can we find a quadratic inequality for each region of the Venn diagram?

The regions are defined as follows.

A: The solution set is a subset of $x≤1$.

B: The solutions are given by $a≤x≤b$ where $a$ and $b$ are real numbers.

C: The inequality is satisfied by $x=4$, e.g. $x=4$ satisfies the inequality $x≥2$.

Here are some possible inequalities. Start by placing these into the correct region of the Venn diagram.

$x^2≤9$

$11x≥2x^2$

$x^2+3≥2$

$3x^2≥21x-30$

$x^2≤-x$

$x^2≤x-2$

$6x^2-1≥5x$

$-2x^2≤x-6$