Solving One-Step Equations • Topic 3 of 3

Checking Solutions by Substitution

Why Check Your Answer?

Substituting your solution back into the original equation verifies that you solved correctly!

Steps to Check:

Take the original equation
Replace the variable with your solution
Calculate both sides
If both sides are equal, your solution is correct!

Example: Solve x + 8 = 15 → x = 7

Check:

Original: x + 8 = 15
Substitute x=7: 7 + 8 = 15
15 = 15 ✓ Correct!

CHECKING PROCESS - FLOWCHART:

    Solve equation → Get solution
           │
           ▼
    Substitute into original equation
           │
           ▼
    Calculate left side and right side
           │
           ▼
    Are they equal?
         │
    ┌────┴────┐
    │         │
   YES        NO
    │         │
    ▼         ▼
Correct   Check work
solution   and retry


CHECKING MULTIPLICATION EQUATION:

    Original: 3z = 18
    Solution: z = 6
    
    Check: 3(6) = 18
           18 = 18 ✓


CHECKING DIVISION EQUATION:

    Original: m/2 = 7
    Solution: m = 14
    
    Check: 14/2 = 7
           7 = 7 ✓


COMMON MISTAKES TO CHECK:

    Mistake: x - 5 = 12 → x = 7 (should be 17)
    Check: 7 - 5 = 2 ≠ 12 → Wrong!
    
    Mistake: 4x = 24 → x = 8 (should be 6)
    Check: 4(8) = 32 ≠ 24 → Wrong!

Solved Examples

Worked Example

Solve and check: x + 12 = 30

Solution

Solve: x = 30 - 12 = 18
Check: 18 + 12 = 30 ✓
Answer: x = 18

Worked Example

Solve and check: y - 9 = 15

Solution

Solve: y = 15 + 9 = 24
Check: 24 - 9 = 15 ✓
Answer: y = 24

Worked Example

Solve and check: 6a = 54

Solution

Solve: a = 54 ÷ 6 = 9
Check: 6(9) = 54 ✓
Answer: a = 9

Worked Example

Solve and check: b/5 = 8

Solution

Solve: b = 8 × 5 = 40
Check: 40/5 = 8 ✓
Answer: b = 40

Key Points

Always check your solution by substituting back
Checks prevent careless mistakes
Both sides must be equal
If check fails, re-solve carefully
Show check work for full credit

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.To check a solution, you ___ it back into the equation.

Explanation: Substitute.

Q2.If both sides are equal, the solution is:

Explanation: Correct.

Q3.Does $x=4$ satisfy $2x+1=9$?

Explanation: $9=9$.

Q4.A wrong solution makes the two sides:

Explanation: Unequal.

Practice more MCQs → 📝 Assignment · 35 marks