📘 10 Exercices : Équations
Avec Solutions Étapes par Étapes • 1ère Année Collège (1AC)
✏️ Exercice 1 : Équations simples (x + a = b)
1. \( x + 4 = 9 \) →
2. \( x + 6 = 11 \) →
3. \( x – 3 = 7 \) →
4. \( x + 2 = 10 \) →
5. \( x – 5 = 8 \) →
1. \( x = 9 – 4 = 5 \)
2. \( x = 11 – 6 = 5 \)
3. \( x = 7 + 3 = 10 \)
4. \( x = 10 – 2 = 8 \)
5. \( x = 8 + 5 = 13 \)
✏️ Exercice 2 : Équations (ax = b)
1. \( 2x = 14 \) →
2. \( 3x = 18 \) →
3. \( 5x = 25 \) →
4. \( 4x = 16 \) →
5. \( 6x = 30 \) →
1. \( x = 14 \div 2 = 7 \)
2. \( x = 18 \div 3 = 6 \)
3. \( x = 25 \div 5 = 5 \)
4. \( x = 16 \div 4 = 4 \)
5. \( x = 30 \div 6 = 5 \)
✏️ Exercice 3 : Équations (x – a = b)
1. \( x – 4 = 5 \) →
2. \( x – 7 = 3 \) →
3. \( x – 2 = 9 \) →
4. \( x – 8 = 4 \) →
5. \( x – 1 = 12 \) →
On ajoute \( a \) des deux côtés :
1. \( x = 5 + 4 = 9 \)
2. \( x = 3 + 7 = 10 \)
3. \( x = 9 + 2 = 11 \)
4. \( x = 4 + 8 = 12 \)
5. \( x = 12 + 1 = 13 \)
✏️ Exercice 4 : Vrai ou Faux
1. \( x + 5 = 12 \) → \( x = 7 \) →
2. \( 2x = 10 \) → \( x = 8 \) →
3. \( x – 4 = 6 \) → \( x = 10 \) →
4. \( 3x = 15 \) → \( x = 5 \) →
5. \( x + 9 = 15 \) → \( x = 5 \) →
1. \( 7 + 5 = 12 \) → vrai
2. \( 2 \times 8 = 16 \neq 10 \) → faux
3. \( 10 – 4 = 6 \) → vrai
4. \( 3 \times 5 = 15 \) → vrai
5. \( 5 + 9 = 14 \neq 15 \) → faux
✏️ Exercice 5 : Équations (x/a = b)
1. \( \dfrac{x}{2} = 6 \) →
2. \( \dfrac{x}{3} = 7 \) →
3. \( \dfrac{x}{4} = 5 \) →
4. \( \dfrac{x}{5} = 4 \) →
5. \( \dfrac{x}{6} = 3 \) →
On multiplie les deux côtés par le dénominateur :
1. \( x = 6 \times 2 = 12 \)
2. \( x = 7 \times 3 = 21 \)
3. \( x = 5 \times 4 = 20 \)
4. \( x = 4 \times 5 = 20 \)
5. \( x = 3 \times 6 = 18 \)
✏️ Exercice 6 : Problèmes
1. Un nombre + 7 = 15. Quel est ce nombre ? →
2. Le double d’un nombre = 16. Quel est ce nombre ? →
3. Un nombre moins 6 = 9. Quel est ce nombre ? →
4. Le tiers d’un nombre = 8. Quel est ce nombre ? →
5. Un nombre × 5 = 35. Quel est ce nombre ? →
1. \( x + 7 = 15 \Rightarrow x = 8 \)
2. \( 2x = 16 \Rightarrow x = 8 \)
3. \( x – 6 = 9 \Rightarrow x = 15 \)
4. \( \dfrac{x}{3} = 8 \Rightarrow x = 24 \)
5. \( 5x = 35 \Rightarrow x = 7 \)
✏️ Exercice 7 : Équations à deux étapes
1. \( 2x + 3 = 11 \) →
2. \( 3x – 4 = 11 \) →
3. \( 4x + 5 = 17 \) →
4. \( 5x – 6 = 19 \) →
5. \( 2x + 7 = 15 \) →
\( 2x + 3 = 11 \)
\( 2x = 11 – 3 = 8 \)
\( x = 8 \div 2 = 4 \)
(Similaire pour les autres)
✏️ Exercice 8 : Équations avec parenthèses
1. \( 2(x + 3) = 10 \) →
2. \( 3(x – 2) = 12 \) →
3. \( 4(x + 1) = 16 \) →
4. \( 5(x – 3) = 20 \) →
5. \( 2(x + 5) = 18 \) →
\( 2(x + 3) = 10 \)
\( x + 3 = 5 \)
\( x = 5 – 3 = 2 \)
(Diviser d’abord par 2, puis isoler x)
✏️ Exercice 9 : Trouver l’inconnue
1. \( x + 9 = 17 \) →
2. \( 4x = 32 \) →
3. \( x – 8 = 12 \) →
4. \( \dfrac{x}{4} = 7 \) →
5. \( 3x + 4 = 19 \) →
1. \( x = 17 – 9 = 8 \)
2. \( x = 32 \div 4 = 8 \)
3. \( x = 12 + 8 = 20 \)
4. \( x = 7 \times 4 = 28 \)
5. \( 3x = 15 \Rightarrow x = 5 \)
✏️ Exercice 10 : Révision Générale
1. \( x + 6 = 14 \) →
2. \( 2x = 18 \) →
3. \( x – 7 = 13 \) →
4. \( \dfrac{x}{6} = 5 \) →
5. \( 4(x + 2) = 24 \) →
1. \( x = 14 – 6 = 8 \)
2. \( x = 18 \div 2 = 9 \)
3. \( x = 13 + 7 = 20 \)
4. \( x = 5 \times 6 = 30 \)
5. \( x + 2 = 6 \Rightarrow x = 4 \)
