Interactive Linear Equations in One Variable Worksheet

Chapter 2: Linear Equations in One Variable (Moderate Level)

Linear equations are algebraic equations where the highest power of the variable is 1. Let's master solving them step by step.

First, let's practice basic linear equation solving techniques.

1. Solve: 4x – 7 = 13 Answer: x =

2. Find the value of x: x2 + 3 = 6 Answer: x =

3. Solve: 3(x – 4) = 0 Answer: x =

4. If 5x – 2 = 3, what is the value of x? Answer: x =

5. Find x: 2x + 5 = x + 11 Answer: x =

6. If x – 1 = 3x + 5, find x. Answer: x =

7. Solve: 6x – 2 = 4x + 10 Answer: x =

8. If 3x + 2 = 2x + 5, then find x. Answer: x =

9. Solve: 3x + 4 = 2x – 6 Answer: x =

10. Solve: x – 4 = 4x – 10 Answer: x =

Drag each equation to its correct solving method:

Part B: Short Answer Questions (2 Marks Each)

1. If 3(x – 2) + 5 = 2(x + 1) – 4, find x. Answer: x =

2. Solve: 5x – (3x + 2) = 3 – (x – 1). Answer: x =

3. Rectangle perimeter is 50 cm. Length is 4 cm more than twice breadth. Find dimensions.

breadth = cm

Length = cm

4. Sum of three consecutive integers is 90. Find the integers.

The three consecutive integers are , ,

Part C: Long Answer Questions (4 Marks Each)

1. Wire is 42 cm long, cut into two parts. One part is 23 of the other. Find lengths.

L1 = cm (Hint: enter the shorter length)

L2 = cm (Hint: enter the longer length)

2. Father and son's ages sum to 45. Five years ago, father was 4 times son's age. Find present ages.

Son’s age = years

Father’s age = years

3. Shopkeeper sells chair at ₹ 60 profit. Cost = x, Selling = x + 60. Discount ₹ 40 on marked price. Find marked price.

Marked price = ₹ x + 100x - 100

4. ₹ 480 divided between A and B such that 4×A's share = 5×B's share. Find shares.

A's share = ₹

B's share= ₹

Test your understanding with these multiple choice questions:

For each question, click on the correct answer:

1. If x + 1 = 2x – 3, then x =

(a) x = –2 (b) x = 4 (c) x = –4 (d) x = 2

Good! The value of x = 4.

2. The equation 3x+52 = x−13 can be written as:

(a) 6x + 10 = 2x – 2 (b) 3x + 5 = 2x – 1 (c) 9x + 15 = 2x – 2 (d) None of the above

Excellent! The equation is 9x + 15 = 2x – 2.

3. Which of the following is NOT a linear equation?

(a) x + 2 = 5 (b) 3x – 7 = 8 (c) x2 + 1 = 5 (d) x2 = 3

The equation x2 + 1 = 5 is not linear.

4. What is the solution of: x3 – 4 = 2?

(a) 18 (b) –18 (c) –6 (d) 6

The solution is x = 18.

5. If x = 2 satisfies 4x – 1 = y, then y =

(a) 6 (b) 7 (c) 8 (d) 5

The solution is y = 7.