Name:_____________________________________________
Date:___________
Discovery Activity: Graphing Inequalities
Directions: For each inequality given below, answer the questions given and use
your answers to graph the solution set to the inequality.
1. Inequality #1: 𝒙 > −𝟑
a) State five numbers that are solutions to the inequality above. Draw a
closed circle on each of these numbers on the number line below.
b) Is the number -3 a solution to the inequality? If it is not a solution, draw an
open circle around -3 on the number line. If it is a solution, draw a circle
around -3 on the number line and shade this circle in.
c) Are all the circles that you drew in letter a to the right or the left of -3?
 If your answer was “left”, starting at either the closed or open circle
that you drew on -3, shade everything to the left of -3 on the
number line.
 If your answer was “right”, starting at either the closed or the
open circle that you drew on -3, shade everything to the right of -3
on the number line.
2. Inequality #2: 𝒙 ≥ 𝟐
a) State five numbers that are solutions to the inequality above. Draw a
closed circle on each of these numbers on the number line below.
b) Is the number 2 a solution to the inequality? If it is not a solution, draw an
open circle around 2 on the number line. If it is a solution, draw a circle
around 2 on the number line and shade this circle in.
c) Are all the circles that you drew in letter a to the right or the left of 2?
 If your answer was “left”, starting at either the closed or open circle
that you drew on 2, shade everything to the left of 2 on the number
line.
 If your answer was “right”, starting at either the closed or the
open circle that you drew on 2, shade everything to the right of 2 on
the number line.
3. Inequality #3: 𝒙 < 𝟓
a) State five numbers that are solutions to the inequality above. Draw a
closed circle on each of these numbers on the number line below.
b) Is the number 5 a solution to the inequality? If it is not a solution, draw an
open circle around 5 on the number line. If it is a solution, draw a circle
around 5 on the number line and shade this circle in.
c) Are all the circles that you drew in letter a to the right or the left of 5?
 If your answer was “left”, starting at either the closed or open circle
that you drew on 5, shade everything to the left of 5 on the number
line.
 If your answer was “right”, starting at either the closed or the
open circle that you drew on 5, shade everything to the right of 5 on
the number line.
4. Inequality #4: 𝒙 ≤ −𝟏
a) State five numbers that are solutions to the inequality above. Draw a
closed circle on each of these numbers on the number line below.
b) Is the number -1 a solution to the inequality? If it is not a solution, draw an
open circle around -1 on the number line. If it is a solution, draw a circle
around -1 on the number line and shade this circle in.
c) Are all the circles that you drew in letter a to the right or the left of -1?
 If your answer was “left”, starting at either the closed or open circle
that you drew on -1, shade everything to the left of -1 on the
number line.
 If your answer was “right”, starting at either the closed or the
open circle that you drew on -1, shade everything to the right of -1
on the number line.