Question

Choose the correct description of the graph of the compound inequality: x − 2 > −3 and 3x less than or equal to 12 A number line with an open circle on −1, shading to the left, and a closed circle on 4, shading to the right A number line with a closed circle on −1, shading to the left, and an open circle on 4, shading to the right A number line with an open circle on −1, a closed circle on 4, and shading in between A number line with a closed circle on −1, an open circle on 4, and shading in between

Answer 1

The two inequalities translate to the following system:

$\begin{cases} x - 2 > -3\\ 3x \leq 12 \end {cases}$

Each inequality yields the following solution:

$\begin{cases} x > -1\\ x \leq 4 \end {cases}$

So, we want a number to be (strictly) more than one, and less than or equal to 4. You can write this in many methods, the most common are $(1,4]$ or [/tex] 1<x\leq 4 [/tex].

Usually, on number lines, we draw an open circle on excluded values, and a closed circle on included ones. So, we want an open circle on 1, closed on 4, and shaded between.