IB MYP 4-5 Maths- Representing and solving inequalities - Study Notes - New Syllabus
IB MYP 4-5 Maths- Representing and solving inequalities – Study Notes
- Representing and solving inequalities
IB MYP 4-5 Maths- Representing and solving inequalities – Study Notes – All topics
Representing and Solving Inequalities
Representing and Solving Inequalities
An inequality shows that one value is greater than or less than another. It uses symbols instead of an equals sign.
Symbols used in inequalities:
| Property | Description |
|---|---|
| \( a < b \) | \( a \) is less than \( b \) |
| \( a > b \) | \( a \) is greater than \( b \) |
| \( a \leq b \) | \( a \) is less than or equal to \( b \) |
| \( a \geq b \) | \( a \) is greater than or equal to \( b \) |
Representing inequalities on a number line:
- Use a hollow/open circle for \( < \) or \( > \)
- Use a filled/closed circle for \( \leq \) or \( \geq \)
- Draw an arrow in the direction of the solution
| Symbol | Words | Example |
|---|---|---|
| \( > \) | Greater than |  |
| \( < \) | Less than |  |
| \( \geq \) | Greater than or equal to |  |
| \( \leq \) | Less than or equal to |  |
Solving inequalities:
Follow the same steps as solving equations, but remember:
- If you multiply or divide both sides by a negative number, reverse the inequality sign.
Example:
Solve the inequality: \( 2x + 5 < 11 \)
▶️ Answer/Explanation
Subtract 5 from both sides
\( 2x < 6 \)
Divide both sides by 2
\( x < 3 \)
Example:
Solve and graph the inequality: \( x \geq -2 \)
▶️ Answer/Explanation
Solution is already simplified
Inequality: \( x \geq -2 \)
Represent on number line (description)
Draw a number line with a closed circle at \( -2 \), and an arrow extending to the right.
Example:
Solve: \( -3x > 9 \)
▶️ Answer/Explanation
Divide both sides by -3 (remember to reverse the sign!)
\( x < -3 \)
Compound Inequalities
A compound inequality has two inequalities joined by “and” or “or”.
- “and”: The solution must satisfy both inequalities (intersection)
- “or”: The solution satisfies at least one of the inequalities (union)
Example:
Solve the compound inequality: \( -2 \leq x + 3 < 5 \)
▶️ Answer/Explanation
Subtract 3 from all three parts of the inequality
\( -2 – 3 \leq x + 3 – 3 < 5 – 3 \)
\( -5 \leq x < 2 \)
Represent the solution
A number line with a filled circle at -5 and an open circle at 2, shading between them.
Example:
A student needs at least 50 marks to pass a test, and the maximum possible score is 80. Write and solve an inequality for the number of marks, \( x \), the student can get if they pass.
▶️ Answer/Explanation
Translate the conditions into an inequality
Passing score means: \( x \geq 50 \)
Maximum possible: \( x \leq 80 \)
Write the compound inequality
\( 50 \leq x \leq 80 \)
Represent
On a number line: Filled circles at 50 and 80, with shading in between.
Double Inequalities
A double inequality is a compound inequality written as a single expression with three parts, such as:
\( a \leq x < b \)
This means the variable \( x \) is between two values: it satisfies both inequalities simultaneously.
To solve double inequalities:
- Perform the same operation on all three parts at once (e.g., subtracting, adding, multiplying/dividing).
- Important: If you multiply or divide all parts by a negative number, reverse the inequality signs.
Example:
Solve the inequality: \( -4 \leq 2x < 6 \)
▶️ Answer/Explanation
Divide all parts of the inequality by 2
\(\frac{-4}{2} \leq \frac{2x}{2} < \frac{6}{2}\)
\(-2 \leq x < 3\)
Example:
Solve the inequality: \( 10 > -x + 2 \geq 4 \)
▶️ Answer/Explanation
Subtract 2 from all three parts
\( 10 – 2 > -x + 2 – 2 \geq 4 – 2 \)
\( 8 > -x \geq 2 \)
Multiply all parts by -1 (reverse all signs)
\( -8 < x \leq -2 \)
