Inéquations du Premier Degré offers a comprehensive set of 30 progressively challenging exercises focused on solving linear inequalities. Designed for students learning algebra, this resource covers basic to advanced levels, including direct resolutions and techniques for handling parentheses and fractions. Ideal for high school mathematics courses, it provides clear instructions and examples to enhance problem-solving skills. Each exercise is structured to build confidence and understanding in handling inequalities effectively.

Key Points

  • Includes 30 exercises on linear inequalities across three difficulty levels.
  • Covers techniques for solving basic, intermediate, and advanced inequalities.
  • Designed for high school students studying algebra and preparing for exams.
  • Provides clear instructions and examples for effective learning.
irem
2 pages
Language:French
Type:Worksheet
Math
irem
2 pages
Language:French
Type:Worksheet
Math
137
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INÉQUATIONS DU PREMIER DEGRÉ
Fiche d'exercices d'entraînement — 30 Énoncés Progressifs
Rappel important pour la résolution :
Quand on multiplie ou qu'on divise les deux membres d'une inéquation par un nombre
négatif
, on doit
changer le sens
de l'inégalité.
Niveau 1 : Inéquations de base (Résolution directe en 1 ou 2 étapes)
1) x + 5 > 8
2) x - 3 ≤ 7
3) 2x < 10
4) 3x ≥ -12
5) x + 7 < 2
6) -4x ≤ 20
7) x - 6 > -9
8) 5x ≥ 0
9) -x < 4
10) x + 1,5 ≤ 4,5
Niveau 2 : Inéquations intermédiaires (Regroupement des termes)
11) 2x + 4 > 12
12) 3x - 7 ≤ 8
13) 5x + 2 < 3x + 10
14) 7x - 5 ≥ 4x + 7
15) 1 - 2x ≤ 9
16) 4x - 3 < 6x + 5
17) -3x + 5 > -4
18) 8 - x ≥ 2x - 1
19) 10x - 4 ≤ 7x + 5
20) 2,5x + 1 > 6
Mathématiques — Niveau Moyen Page 1 / 2
Niveau 3 : Inéquations avancées (Parenthèses et fractions simples)
21) 2(x + 3) ≤ 14
22) 3(2x - 1) > 9
23) -(x - 5) < 2
24) 4(x - 2) ≥ 2(x + 4)
25) x/2 + 3 < 7
26) 2x/3 ≥ 4
27) 5 - 2(x + 1) ≤ 3
28) (x - 1)/4 > 2
29) 3(x + 4) - x ≤ 2x + 12
30) x/3 - 1 ≥ x/2
Mathématiques — Niveau Moyen Page 2 / 2
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FAQs

what are the exercises in 30 inéquations du premier degré

The document '30 Inéquations du Premier Degré - Exercices Progressifs' contains a variety of exercises designed to help students practice solving first-degree inequalities.

  • Level 1: Basic inequalities requiring direct resolution.
  • Level 2: Intermediate inequalities that involve regrouping terms.
  • Level 3: Advanced inequalities that include parentheses and simple fractions.

how to solve inéquations du premier degré

To solve 'inéquations du premier degré', you follow specific steps based on the type of inequality.

  • Identify the inequality type (e.g., >, <, ≥, ≤).
  • Isolate the variable on one side, ensuring to reverse the inequality sign if multiplying or dividing by a negative number.
  • Check the solution by substituting values back into the original inequality.

what is the importance of inéquations du premier degré

'Inéquations du premier degré' are crucial in mathematics as they form the foundation for understanding more complex algebraic concepts.

  • They help develop problem-solving skills.
  • They are essential for advanced studies in calculus and statistics.
  • Understanding these inequalities is vital for real-world applications, such as in economics and engineering.

examples of inéquations du premier degré

The document provides numerous examples of 'inéquations du premier degré' to illustrate various solving techniques.

  • Example 1: x + 5 > 8
  • Example 2: 2x < 10
  • Example 3: 4(x - 2) ≥ 2(x + 4)

what are the levels of difficulty in 30 inéquations du premier degré

'30 Inéquations du Premier Degré - Exercices Progressifs' categorizes exercises into three levels of difficulty.

  • Level 1: Basic inequalities that require one or two steps to solve.
  • Level 2: Intermediate inequalities that involve more complex manipulation of terms.
  • Level 3: Advanced inequalities including parentheses and fractions, requiring a deeper understanding of algebra.

how to approach solving advanced inéquations du premier degré

When tackling advanced 'inéquations du premier degré', it's essential to follow a structured approach.

  • Begin by simplifying both sides of the inequality.
  • Use algebraic techniques to isolate the variable.
  • Pay attention to the rules regarding the inequality sign when multiplying or dividing by negative numbers.