Instructions: Answer all 15 questions. Write your answers in the spaces provided.
For number line questions: use an open circle for strict inequalities ($<$ and $>$) and a closed circle for inclusive inequalities ($\leq$ and $\geq$).
Section A — Recall Questions 1–5
1.State the meaning of the symbol $\geq$ in words.
2.What type of circle is used on a number line to represent a strict inequality?
3.State the two inequality symbols that require a closed circle on a number line.
4.On a number line, in which direction does the line extend from the circle for the inequality $x > 5$?
5.What does a closed circle at a value on a number line tell you about that value?
Section B — Application Questions 6–10
6.
Write the inequality shown on this number line.
7.
Write the inequality shown on this number line.
8.
Write the inequality shown on this number line.
9.Describe how to represent the inequality $x \geq -3$ on a number line. State: the type of circle used, where to place it, and the direction the line goes.
10.
Write the inequality shown on this number line.
Section C — Challenge Questions 11–15
11.Write the inequality shown by each of the following number lines.
(a)
(b)
(c)
12.For the inequality $-4 \leq x < 1$:
(a)
What type of circle is used at $x = -4$? Explain why.
(b)
What type of circle is used at $x = 1$? Explain why.
(c)
Is the value $x = 1$ included in this inequality? Give a reason.
13.A student draws a number line to show $x > 2$. They use a closed circle at 2 and shade to the right.
(a)
Identify the mistake in the student’s diagram.
(b)
State what the correct circle should be and explain why.
14.
A number line shows a closed circle at $-3$ and an open circle at $0$, with a line connecting them.
(a)
Write the inequality shown.
(b)
Is $x = -3$ a solution to this inequality? Give a reason.
(c)
Is $x = 0$ a solution to this inequality? Give a reason.
(d)
Write one value of $x$ that satisfies this inequality.
15.Answer the following questions about inequalities and number lines.
(a)
A number line has a closed circle at 1 with the line going to the right. Write the inequality this represents.
(b)
Write an inequality that would be shown with an open circle at 1 with the line going to the left.
(c)
Explain how the two inequalities from (a) and (b) differ in terms of whether $x = 1$ is included.
