Algebra - How to graph an inequality with a number line

Which line plot corresponds to the inequality below?

$3x+2\geq 11$

Explanation

A closed circle indicates "greater than or equal to" or "less than or equal to," while and open circle indicates "greater than" or "less than". We can tell from the inequality that our line plot will only have closed circles, as the only symbol is "greater than or equal to."

$3x+2\geq11$

Subtract from both sides.

$3x+2-2\geq11-2$

$3x\geq 9$

Divide both sides by .

$\frac{3x}{3}\geq\frac{9}{3}$

$x\geq 3$

Our plot will show a closed circle on , and extend infinitvely in the positive direction.

What inequality is represented by the number line?

$\small x<-4\ or$ $x\geq 2$

$\small -4<x\leq2$

$\small -4\leq x <2$

$\small x\leq4\ or\ x>2$

Explanation

An open circle indictes "less than" or "greater than," while a closed circle indicates "greater than or equal to" or "less than or equal to".

This number line includes values that are less than $\small -4$ or greater than or equal to $\small 2$ . Note how $\small -4$ has an open circle, while $\small 2$ has a closed circle.

How to graph an inequality with a number line

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