Last reviewed: 11 November 2026
Updated November 2026. These Grade 7 linear inequalities notes show how to use inequality symbols, how to form simple and compound linear inequalities in one unknown, and how to illustrate them on a number line. An equation says two sides are equal. An inequality says one side is greater than, less than, or at least as large as the other, as in x + 3 < 10.
The examples are original practice for Kenyan junior school learners, not an official paper. They follow the Grade 7 Mathematics algebra sub-strand on linear inequalities in the KICD Grade Seven curriculum designs. Graphing inequalities on the Cartesian plane is later work, in the Grade 9 linear inequalities notes. For Grade 7 topics overall, use the Grade 7 mathematics revision guide and the Grade 7 notes hub.
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Inequality Symbols and Simple Inequalities
The four symbols you need are:
- < less than
- > greater than
- ≤ less than or equal to (at most)
- ≥ greater than or equal to (at least)
“There are fewer than 10 learners in the group” can be written n < 10. “A child must be at least 12 years old” can be written a ≥ 12. To illustrate a simple inequality on a number line, mark the boundary number with an open circle if it is not included (< or >) and a closed (filled) circle if it is included (≤ or ≥), then draw an arrow over all the numbers that work. OpenStax Elementary Algebra’s section on linear inequalities uses the same open- and closed-circle convention.
Worked example: a simple inequality
Solve x + 3 < 10 and show the answer on a number line. Subtract 3 from both sides: x < 7. Draw an open circle at 7 and an arrow to the left. The number 7 itself is not a solution, because 7 + 3 = 10 is not less than 10. The number 6 is a solution, because 6 + 3 = 9, which is less than 10.
Solve 2x ≥ 10. Divide both sides by 2: x ≥ 5. Draw a closed circle at 5 and an arrow to the right. The number 5 is included.
Compound Inequalities in One Unknown
A compound inequality joins two conditions about the same unknown. 3 < x ≤ 8 means x is greater than 3 and at the same time at most 8. On the number line that is an open circle at 3, a closed circle at 8, and a shaded segment between them. −2 ≤ x < 5 is a closed circle at −2, an open circle at 5, and the segment joining them.
Worked example
A club accepts learners who are more than 10 years old but not older than 14. If a is the age in whole years, then 10 < a ≤ 14. Possible whole-number ages are 11, 12, 13 and 14.
Form an inequality for “a number x is at least −1 and less than 4”: −1 ≤ x < 4. On the number line, close the circle at −1 and leave the circle at 4 open.
Original Practice Questions With Worked Answers
- Write a symbol for “at most 20”. ≤ 20.
- Solve x − 4 > 3 and describe the number line. x > 7: open circle at 7, arrow right.
- Solve 5x ≤ 20. x ≤ 4: closed circle at 4, arrow left.
- Illustrate −3 < x ≤ 2. Open circle at −3, closed circle at 2, segment between them.
- List the whole-number solutions of 0 ≤ n < 4. 0, 1, 2 and 3.
- A learner marks an open circle at 5 for x ≥ 5. What should change? The circle should be closed, because 5 itself satisfies x ≥ 5.
Cover the answers and sketch each number line before checking. Solving related equations first can help; see the Grade 7 linear equations notes. For timed practice use the Grade 7 CBC Challenge. These notes are free; full revision access is available with the KSh 20 Day Pass or the KSh 500 Monthly Pass.
Frequently Asked Questions
What do the four inequality symbols mean?
< means less than, > means greater than, ≤ means less than or equal to, and ≥ means greater than or equal to. “At least 12” is ≥ 12 and “at most 20” is ≤ 20.
When is the circle on a number line open or closed?
Use an open circle for < or >, because the boundary number is not included. Use a closed circle for ≤ or ≥, because the boundary number is included.
What is a compound inequality?
It is two conditions about the same unknown joined together, such as 3 < x ≤ 8. Both conditions must be true at the same time.
Do Grade 7 inequalities use Cartesian graphs?
Grade 7 illustrates inequalities on a number line. Drawing regions on the Cartesian plane is part of the Grade 9 sub-strand.