Inequalities

Syllabus tag: Kenya CBC | Grade 6 Mathematics | Strand 1.0 Numbers | Sub-Strand 1.6 Inequalities (8 Lessons)

Lesson objectives

By the end of this topic, you will be able to:

• Form simple inequalities in one unknown from real-life situations
• Simplify inequalities in one unknown
• Solve simple inequalities in one unknown
• Appreciate the use of inequalities in real life

Inequalities

An equation says two things are equal. An inequality says one is bigger or smaller than the other.

a) The symbols

The symbol < means "is less than". The symbol > means "is greater than".

So 3 < 8 says three is less than eight. And 9 > 4 says nine is greater than four.

The wide end always faces the bigger number. The point faces the smaller one.

b) From real situations

A bus carries fewer than 30 people. If p is the number of people, then p < 30.

A child must be more than 5 years old to join. If a is the age, then a > 5.

Name the letter and say what it stands for, then write the inequality.

c) Showing it on a number line

An open circle marks the number itself, because it is not included.

The line is drawn towards all the values that work. Here it goes left, because x is less than 7.

d) Simplifying

Collect like terms first, exactly as you would in an equation.

So 2x + 3x < 20 becomes 5x < 20.

e) Solving

Do the same thing to both sides until the letter is alone.

Take away 3 from both sides, or divide both sides by the same number. The inequality stays true.

The answer is not one number. For x < 7, every number below 7 works.

f) Checking

Pick a number from your answer and try it in the original.

For x < 7, try x = 5. Then 5 + 3 = 8, and 8 is indeed less than 10. The answer works.

Then try a number outside the answer, such as x = 9. Then 9 + 3 = 12, which is not less than 10. That confirms it as well.

g) Where this is used

A lift has a weight limit. A shop offers a discount above a certain spend. A game has a minimum age. Each of these is an inequality.

Words to know

• Inequality — a mathematical statement comparing two expressions using >, <, ≥, or ≤, instead of an equals sign.
• Unknown — the letter representing an unknown value (e.g. x or y).
• Solve — to find every value of the unknown that makes the inequality true.

:::checkpoint Check yourself

1. Write in symbols: y is greater than 12.
2. Simplify 4x + 2x < 18.
3. Solve x + 6 < 15.
4. Which circle do you draw for x < 4, open or filled? :::

Bridge to practice

Try the exercises below — forming, simplifying, and solving inequalities, plus real-life situations that translate directly into one, the same four skills covered above.