An open sentence is a mathematical statement with a letter (unknown).

Solving an open sentence means finding the value of the letter that makes the statement true.

Two arithmetic operations involve any combination of addition, subtraction, multiplication, or division in one sentence.

1. Identify the unknown (usually represented by a letter, e.g., x).


2. Follow the order of operations (BODMAS):
   
   
   • Brackets → Orders (powers, roots) → Division → Multiplication → Addition → Subtraction
   
   
3. Undo operations in reverse order (from the operation closest to the unknown last).


4. Check your answer by substituting it back into the original sentence.

Example 1

Solve: 3x + 5 = 20

Step 1: Subtract 5 from both sides:

3x + 5 - 5 = 20 - 5 → 3x = 15

Step 2: Divide both sides by 3:

x = 15 ÷ 3 = 5

Check: 3 × 5 + 5 = 15 + 5 = 20

Example 2

Solve: 2x - 7 = 9

Step 1: Add 7 to both sides:

2x - 7 + 7 = 9 + 7 → 2x = 16

Step 2: Divide by 2:

x = 16 ÷ 2 = 8

Check: 2 × 8 - 7 = 16 - 7 = 9

Example 3

Solve: 5 + 4x = 21

Step 1: Subtract 5:

4x = 21 - 5 = 16

Step 2: Divide by 4:

x = 16 ÷ 4 = 4

Check: 5 + 4 × 4 = 5 + 16 = 21

Example 4

Solve: 6x - 9 = 15

Step 1: Add 9:

6x = 15 + 9 = 24

Step 2: Divide by 6:

x = 24 ÷ 6 = 4

Check: 6 × 4 - 9 = 24 - 9 = 15

Example 5

Solve: 3x + 12 = 27

Step 1: Subtract 12:

3x = 27 - 12 = 15

Step 2: Divide by 3:

x = 15 ÷ 3 = 5

Check: 3 × 5 + 12 = 15 + 12 = 27

Example 6

Solve: 7x - 14 = 21

Step 1: Add 14:

7x = 21 + 14 = 35

Step 2: Divide by 7:

x = 35 ÷ 7 = 5

Check: 7 × 5 - 14 = 35 - 14 = 21

Summary

• Always undo the operations step by step.


• Follow BODMAS to ensure correct order.


• Substitute the solution back into the open sentence to verify your answer.