Algebra Worksheet – Class 6
Name: _____________________
Date: _____________________
A. Identify the Variable
- 5 + x = 12 → Variable = ______
- y – 7 = 15 → Variable = ______
- 3a + 4 = 19 → Variable = ______
- b ÷ 5 = 6 → Variable = ______
- 7 + m = 20 → Variable = ______
B. Simplify the Expressions
- 3x + 5x = ______
- 7a + 4a – 5 = ______
- 2y + 3y + 6 = ______
- 10p – 4p + 9 = ______
- 6m + 2 – 3m + 5 = ______
C. Solve the Equations
- x + 7 = 15 → x = ______
- 3y = 21 → y = ______
- 5a – 10 = 20 → a = ______
- 2b + 6 = 14 → b = ______
- 4m ÷ 2 = 6 → m = ______
D. Word Problems
- A number increased by 12 is 30. Find the number.
- Three times a number is 21. Find the number.
- If 5 less than a number is 16, find the number.
- A rectangle has a length of x + 3 and width 4. If the perimeter is 22, find x.
- John has x marbles. He gives 7 to his friend. If he has 13 left, find x.
E. Bonus Challenge
- Solve for x: 2x + 5 = 17
- Solve for y: 3y – 4 = 11
- Solve for a: 4a + 7 = 31
- Solve for b: 5b ÷ 5 + 2 = 10
- Solve for m: 6m – 9 = 15
Answer
A. Identify the Variable
- 5 + x = 12 → Variable = x
- y – 7 = 15 → Variable = y
- 3a + 4 = 19 → Variable = a
- b ÷ 5 = 6 → Variable = b
- 7 + m = 20 → Variable = m
B. Simplify the Expressions
- 3x + 5x = 8x
- 7a + 4a – 5 = 11a – 5
- 2y + 3y + 6 = 5y + 6
- 10p – 4p + 9 = 6p + 9
- 6m + 2 – 3m + 5 = 3m + 7
C. Solve the Equations
- x + 7 = 15 → x = 15 – 7 = 8
- 3y = 21 → y = 21 ÷ 3 = 7
- 5a – 10 = 20 → 5a = 30 → a = 30 ÷ 5 = 6
- 2b + 6 = 14 → 2b = 8 → b = 8 ÷ 2 = 4
- 4m ÷ 2 = 6 → 4m = 12 → m = 12 ÷ 4 = 3
D. Word Problems
- Number + 12 = 30 → Number = 30 – 12 = 18
- 3 × Number = 21 → Number = 21 ÷ 3 = 7
- Number – 5 = 16 → Number = 16 + 5 = 21
- Rectangle: 2(length + width) = 22 → 2(x + 3 + 4) = 22 → 2(x + 7) = 22 → x + 7 = 11 → x = 4
- John’s marbles: x – 7 = 13 → x = 13 + 7 = 20
E. Bonus Challenge
- 2x + 5 = 17 → 2x = 12 → x = 6
- 3y – 4 = 11 → 3y = 15 → y = 5
- 4a + 7 = 31 → 4a = 24 → a = 6
- 5b ÷ 5 + 2 = 10 → b + 2 = 10 → b = 8 → 8
- 6m – 9 = 15 → 6m = 24 → m = 4