Grade 6 Mathematics Algebra – Inequalities Notes
Mathematics — Algebra: Inequalities (Age 11)
What is an inequality?
An inequality shows that two amounts are not equal and tells which is bigger or if one may be equal. Instead of "=", we use symbols such as:
- < (less than). Example: 3 < 5 (3 is less than 5)
- > (greater than). Example: 7 > 2 (7 is greater than 2)
- ≤ (less than or equal to). Example: x ≤ 4 (x is at most 4)
- ≥ (greater than or equal to). Example: y ≥ 0 (y is at least 0)
- ≠ (not equal to). Example: x ≠ 6 (x is not 6)
Reading and writing inequalities
Read x > 3 as "x is greater than 3." Read x ≤ 5 as "x is less than or equal to 5."
Solving simple linear inequalities
We solve inequalities much like equations: do the same operation on both sides. But remember:
If you multiply or divide both sides by a negative number, you must flip the inequality sign.
Example 1: Solve x + 3 > 7
Steps:
Steps:
- Subtract 3 from both sides: x + 3 − 3 > 7 − 3
- So x > 4
Number line for x > 4:
0
1
2
3
○
4
5
6
7
8
The open circle at 4 means 4 is not included. The arrow (→) to the right means numbers bigger than 4.
Example 2: Solve 2x ≤ 10
Steps:
Steps:
- Divide both sides by 2: (2x)/2 ≤ 10/2
- So x ≤ 5
Number line for x ≤ 5:
0
2
4
●
5
6
Filled circle at 5 means 5 is included; shade left for numbers ≤ 5.
Important rule:
If you do this: multiply or divide an inequality by a negative number (e.g. −2), flip the sign.
Example: −2x > 6 → divide by −2 → x < −3 (note the > changed to <)
How to check your answer
Substitute a number from your solution into the original inequality. If it makes the inequality true, the answer is correct.
Check Example 1: x > 4. Try x = 6 → 6 + 3 > 7 → 9 > 7 (true). So x = 6 is in the solution.
Practice
- Solve: x + 5 < 10
- Solve: 3x ≤ 12
- Solve: x − 7 ≥ 2
- Solve: −4x > 8
- Solve and draw on a number line: 2x − 1 < 5
- Write the inequality: "y is at least 9"
Answers
- 1) x < 5
- 2) x ≤ 4
- 3) x ≥ 9
- 4) x < −2 (note the sign flips when dividing by −4)
- 5) 2x − 1 < 5 → 2x < 6 → x < 3 (draw open circle at 3 and shade left)
- 6) y ≥ 9
Tips for learners (Kenyan primary)
- Remember the inequality sign points to the smaller number: 2 < 5 points to 2.
- Always do the same thing to both sides (add, subtract, multiply or divide).
- When multiplying or dividing by a negative, flip the sign.
- Use a number line to show whether a value is included (●) or not (○).
Notes prepared for age 11 — use these for class exercises or revision. Practice more problems and try drawing number lines for each solution.