Linear Equations — Fiche d'exercices de Algebra I

Grades 8–9 Difficulté facile 10 problèmes

A linear equation in one variable has the form $ax + b = c$ , where the variable appears only to the first power. Solving means finding the value of the variable that makes the equation true.

The golden rule of equation solving is balance: whatever you do to one side, do to the other. Work in reverse order of operations — undo addition/subtraction first, then multiplication/division.

When variables appear on both sides, collect them on one side and constants on the other. Always check your answer by substituting into the original equation.

Compétences travaillées

One-step and two-step equations
Equations with variables on both sides
Distributive property in equations
Checking solutions

Nom : Date : Période :

Fiche d'exercices : Linear Equations

Consignes : Résous chaque problème avec soin. Montre clairement tout ton travail. Écris ta réponse finale dans l'espace prévu ou sur une feuille séparée comme indiqué.

1.Solve for $x$ : $3x + 7 = 22$ .

Linear Equations — Fiche d'exercices (suite)

2.Solve for $y$ : $5y - 9 = 2y + 6$ .
3.Solve for $a$ : $4(a - 3) = 2a + 8$ .

Linear Equations — Fiche d'exercices (suite)

4.Solve for $b$ : $\dfrac{b}{5} + 2 = 7$ .
5.Solve for $c$ : $6c + 4 = 2c - 12$ .

Linear Equations — Fiche d'exercices (suite)

6.A number increased by 9 is equal to 24. Find the number.
7.The sum of twice a number and 5 is 19. What is the number?

Linear Equations — Fiche d'exercices (suite)

8.Three times a number, minus 4, is equal to 11. Find the number.
9.A rectangle has a length that is 3 inches more than its width. The perimeter is 30 inches. Find the width and length.

Linear Equations — Fiche d'exercices (suite)

10.Tickets to a play cost $8 for adults and $5 for children. A group of 12 people paid $78 total. How many adults and how many children were in the group?

Corrigé

1.

Subtract 7: $3x = 15$ ; Divide by 3: $x = 5$

Réponse finale : $x = 5$
2.

Subtract $2y$ : $3y - 9 = 6$ ; Add 9: $3y = 15$ ; Divide by 3: $y = 5$

Réponse finale : $y = 5$
3.

Distribute: $4a - 12 = 2a + 8$ ; Subtract $2a$ : $2a - 12 = 8$ ; Add 12: $2a = 20$ ; Divide by 2: $a = 10$

Réponse finale : $a = 10$
4.

Subtract 2: $\dfrac{b}{5} = 5$ ; Multiply by 5: $b = 25$

Réponse finale : $b = 25$
5.

Subtract $2c$ : $4c + 4 = -12$ ; Subtract 4: $4c = -16$ ; Divide by 4: $c = -4$

Réponse finale : $c = -4$
6.

Let $n$ be the number. $n + 9 = 24$ ; Subtract 9: $n = 15$

Réponse finale : The number is 15.

Corrigé (suite)

7.

Let $n$ be the number. $2n + 5 = 19$ ; Subtract 5: $2n = 14$ ; Divide by 2: $n = 7$

Réponse finale : The number is 7.
8.

Let $n$ be the number. $3n - 4 = 11$ ; Add 4: $3n = 15$ ; Divide by 3: $n = 5$

Réponse finale : The number is 5.
9.

Let $w$ be the width. Then length $= w + 3$ . Perimeter: $2w + 2(w + 3) = 30$ ; Simplify: $4w + 6 = 30$ ; Subtract 6: $4w = 24$ ; Divide by 4: $w = 6$ ; Length: $6 + 3 = 9$

Réponse finale : Width = 6 inches, Length = 9 inches.
10.

Let $a$ be number of adults, $c$ be number of children. $a + c = 12$ ; $8a + 5c = 78$ ; From first: $c = 12 - a$ ; Substitute: $8a + 5(12 - a) = 78$ ; $3a + 60 = 78$ ; Subtract 60: $3a = 18$ ; Divide by 3: $a = 6$ ; Then $c = 12 - 6 = 6$

Réponse finale : 6 adults and 6 children.

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Erreurs fréquentes à éviter

Sign errors when moving terms across the equals sign
Dividing only one term instead of the entire side
Forgetting to distribute to every term inside parentheses
Accepting extraneous solutions without checking

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