Sec 2 Maths · Linear equations, inequalities and simultaneous equations

Number lines questions with answers

Practice questions on number lines, from the basics up to exam level, each with a full worked solution. Try them on paper first, then open the solution to check your working.

Worked example

Write down the inequality shown on the number line.

Step 1 of 2

Read the circles

A filled circle means the value is included (

\leq

\geq

); an open circle means it is not (

<

>

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Questions

Question 1Rays to the left or right
Write down the inequality shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $x \geq 5$
Question 2Rays to the left or right
Write down the inequality shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $x > 0$
Question 3Between two values
Write down the inequality shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $5 < x < 7$
Question 4Between two values
Write down the inequality shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $-1 < x < 1$
Question 5List the integers
Write down the integer values of $x$ shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $2 \leq x \leq 6$
3. Step 3: List the integers in that range $2$ , $3$ , $4$ , $5$ , $6$
Question 6List the integers
Write down the integer values of $x$ shown on the number line.
Show the worked solution
1. Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
2. Step 2: Read the direction, and write the inequality $-4 \leq x \leq 1$
3. Step 3: List the integers in that range $-4$ , $-3$ , $-2$ , $-1$ , $0$ , $1$

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Notes: Linear equations, inequalities and simultaneous equations Worksheet with answers (PDF)

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Questions

Question 1Rays to the left or right

Write down the inequality shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $x \geq 5$

Question 2Rays to the left or right

Write down the inequality shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $x > 0$

Question 3Between two values

Write down the inequality shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $5 < x < 7$

Question 4Between two values

Write down the inequality shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $-1 < x < 1$

Question 5List the integers

Write down the integer values of $x$ shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $2 \leq x \leq 6$
Step 3: List the integers in that range $2$ , $3$ , $4$ , $5$ , $6$

Question 6List the integers

Write down the integer values of $x$ shown on the number line.

Show the worked solution

Step 1: Read the circlesA filled circle means the value is included ( $\leq$ or $\geq$ ); an open circle means it is not ( $<$ or $>$ ).
Step 2: Read the direction, and write the inequality $-4 \leq x \leq 1$
Step 3: List the integers in that range $-4$ , $-3$ , $-2$ , $-1$ , $0$ , $1$