Topic Review — Linear Equations

Review Questions

1. Solve each one-step equation: Fluency

   1. x + 8 = 15
   2. m − 4 = 11
   3. 6n = 42
   4. t ÷ 3 = 7
   5. 20 − p = 8
   6. 4w = 36

2. Solve each two-step equation: Fluency

   1. 2x + 5 = 13
   2. 3y − 4 = 14
   3. 4m + 7 = 31
   4. 5k − 6 = 19
   5. 2a + 3 = 3
   6. n ÷ 2 + 4 = 9

3. The sequence 7, 10, 13, 16, … Understanding

   1. What is the common difference (gap) between terms?
   2. Complete a table showing the first 5 terms.
   3. Write a formula for the nth term.
   4. Find the 20th term.

4. Number puzzle: Understanding

   I think of a number, multiply it by 4, then subtract 6. The result is 22.

   1. Write an equation to represent this situation.
   2. Solve the equation to find the number.

5. Solve the following: Problem Solving

   1. Solve: 3(x + 2) = 18
   2. Solve and check your answer: 4x − 3 = 2x + 7
   3. A rectangle has a perimeter of 34 cm. Its length is 3 cm more than its width. Find the width.

6. Write and solve an equation for each situation: Understanding

   1. A number is doubled and then 9 is added. The result is 31. Find the number.
   2. When a number is divided by 5 and 3 is subtracted, the result is 7. Find the number.
   3. Four friends split a restaurant bill equally. Each person pays $17.50. What was the total bill?

7. Solve and check each equation: Fluency

   1. 5(x − 3) = 20
   2. 2(3y + 1) = 14
   3. 3(2m − 5) = 9
   4. 4(n + 2) = 28

8. The sequence 4, 9, 14, 19, … Understanding

   1. Find the common difference.
   2. Write a formula for the nth term.
   3. Is 99 a term in this sequence? Show your working.
   4. What is the 15th term?

9. Solve these equations involving fractions: Fluency

   1. x ÷ 4 + 3 = 8
   2. 2y ÷ 3 = 6
   3. m ÷ 5 − 2 = 3

10. Two friends have a combined age of 28 years. One friend is 4 years older than the other. Problem Solving

    1. Let the younger friend's age be a. Write an equation for the sum of their ages.
    2. Solve the equation to find both ages.
    3. In 3 years time, what will their combined age be?