Solve x + 5 = 12
The Question
Solve: x + 5 = 12
Find the value of x.
Understanding the Equation
An equation is like a balance scale. The equals sign (=) means both sides weigh the same.
- Left side (LHS): x + 5
- Right side (RHS): 12
We need to find what x is. Right now, x + 5 = 12 means: “some number plus 5 equals 12.”
We can guess: what number plus 5 gives 12? 7! Because 7 + 5 = 12.
But let’s also solve it using the proper method — transposing.
Method 1: Transposing
Transposing means moving a term from one side of the equation to the other. When a term crosses the equals sign, its sign changes.
Equation: x + 5 = 12
The +5 is on the left side with x. We want x alone on the left.
Move +5 to the right side. It becomes -5:
x = 12 - 5
x = 7
Method 2: Balancing Method
Think of the equation as a weighing balance. Whatever we do to one side, we must do to the other side too.
To remove the +5 from the left, we subtract 5 from both sides:
x + 5 - 5 = 12 - 5
x + 0 = 7
x = 7
Both methods give the same answer: x = 7.
Verification (Checking the Answer)
Always substitute the answer back into the original equation to verify.
LHS = x + 5 = 7 + 5 = 12
RHS = 12
LHS = RHS ✓
Our answer x = 7 is correct.
Always write the verification step in exams. It earns you marks AND it’s the only way to be sure your answer is correct. If LHS ≠ RHS after substitution, you know to recheck your working.
Key Takeaway
When a term moves from one side of the equation to the other:
- Addition (+) becomes Subtraction (−)
- Subtraction (−) becomes Addition (+)
x + 5 = 12 → x = 12 − 5 = 7
Try These Similar Problems
Problem 1: Solve: y + 9 = 15
Transpose +9 to the right (becomes -9): y = 15 - 9 = 6
Verify: 6 + 9 = 15 ✓
Problem 2: Solve: n + 3 = 3
Transpose +3 to the right: n = 3 - 3 = 0
Verify: 0 + 3 = 3 ✓ (The unknown can be zero!)
Problem 3: “A number increased by 8 gives 20. Find the number.”
Let the number = x. x + 8 = 20 Transpose: x = 20 - 8 = 12
The number is 12. Verify: 12 + 8 = 20 ✓
Exam tip: Questions like “solve x + 5 = 12” may seem too easy for exams, but they’re common in unit tests and as starter questions. The marks are for showing your method and verification — not just writing “7.”