Question

inequalities
the solutions of an inequality are the values that make the inequality
true. they can be graphed on a number line. use a closed circle (•)
for ≤ and ≥ and an open circle (o) for > and <. for example:
x > -2 (\greater than\)
x < -2 (\less than\)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
x ≥ -2 (\greater than or equal to\)
x ≤ -2 (\less than or equal to\)
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
graph the inequality x > 4.
the inequality is read as \x is greater than 4.\ since all numbers to
the right of 4 are greater than 4, you can draw an arrow from 4 to the
right. since 4 is not greater than itself, use an open circle on 4.
-2 -1 0 1 2 3 4 5 6 7 8

1. graph the inequality x ≤ -3.

a. write the inequality in words.
b. will the circle at -3 be open or closed?
c. graph the solution.
-7 -6 -5 -4 -3 -2 -1 0 1 2 3

1. graph the inequality x < 3.

a. write the inequality in words.
b. will the circle at 3 be open or closed?
c. graph the solution.
-4 -3 -2 -1 0 1 2 3 4 5 6

Explanation:

Step1: Solve Question 1a

Translate $x \leq -3$ to words: "x is less than or equal to -3".

Step2: Solve Question 1b

Check inequality symbol: $\leq$ uses closed circle.

Step3: Solve Question 1c

Mark closed circle at -3, draw arrow left.

Step4: Solve Question 2a

Translate $x < 3$ to words: "x is less than 3".

Step5: Solve Question 2b

Check inequality symbol: $<$ uses open circle.

Step6: Solve Question 2c

Mark open circle at 3, draw arrow left.

Answer:

1a. x is less than or equal to -3
1b. closed
1c. Closed circle at -3, arrow pointing left
2a. x is less than 3
2b. open
2c. Open circle at 3, arrow pointing left