AlgèbreFacile
Math Learning PlatformInequalities and Intervals
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📚 algebre
📖 About this lesson
Understand and solve inequalities
Lesson Content
Inequalities and Intervals
What is an inequality?
A comparison instead of equality.
[object Object],:
- •< : less than
- • ,[object Object],
- •≤ : less than or equal
- •≥ : greater than or equal
Solving inequalities
Similar to equations.
[object Object],: x + 3 < 10
x < 10 - 3- •x < 7
💡 Tip
[object Object],: When multiplyingdividing by negative, flip the sign!
[object Object],: -2x < 6
x > -3 (sign flipped!)
Interval notation
Open interval
x > 2: ]2, +∞[
Closed interval
x ≥ 2: [2, +∞[
Compound inequalities
[object Object],: 2 < x < 5
- •x is between 2 and 5
- •Interval: ]2, 5[
Graphing
Number line representation:
- •Open circle: < or >
- •Filled circle: ≤ or ≥
Practical Examples
1
Example 1
📋 Problem
Résoudre : 3x - 5 > 7
✅ Solution
x > 4 ou ]4, +∞[
💡 Explanation
3x > 12, donc x > 4
2
Example 2
📋 Problem
Résoudre : -2x + 6 ≤ 10
✅ Solution
x ≥ -2 ou [-2, +∞[
💡 Explanation
-2x ≤ 4, donc x ≥ -2 (on inverse car division par -2)