Solve 3x - 2 = 13
The Question
Solve: 3x - 2 = 13
This is a two-step equation — we need to do two transpositions to find x.
What Makes This a “Two-Step” Equation?
In x + 5 = 12, there’s only one thing to undo (the +5). Easy.
In 3x - 2 = 13, there are two things happening to x:
- It’s being multiplied by 3.
- Then 2 is subtracted.
We need to undo both, in the right order.
The Strategy
To isolate x (get x alone), we undo the operations in reverse order:
- The last operation done to x was subtracting 2.
- So we undo that first: add 2 (or transpose -2 as +2).
- Then undo multiplying by 3: divide by 3 (or transpose ×3 as ÷3).
Step-by-Step Solution
Equation: 3x - 2 = 13
Step 1: Transpose -2 to the right side (it becomes +2)
3x = 13 + 2
3x = 15
Step 2: Transpose ×3 to the right side (it becomes ÷3)
x = 15 ÷ 3
x = 5
Verification
Substitute x = 5 into the original equation: 3x - 2 = 13
LHS = 3(5) - 2 = 15 - 2 = 13
RHS = 13
LHS = RHS ✓
x = 5 is correct.
Solving Using the Balancing Method
For those who prefer the full balance approach:
Step 1: Add 2 to both sides:
3x - 2 + 2 = 13 + 2 3x = 15
Step 2: Divide both sides by 3:
3x ÷ 3 = 15 ÷ 3 x = 5
Same result — as always.
The general order for solving equations: first handle addition/subtraction (move constants to the other side), then handle multiplication/division (deal with the coefficient of x). Think of it as peeling an onion — outer layers first.
For equations like ax ± b = c:
Step 1: Transpose b → x side becomes ax = c ∓ b Step 2: Transpose a → x = (c ∓ b) ÷ a
Common mistake: Dividing by 3 before transposing the -2.
Wrong approach: 3x - 2 = 13, so 3x = 13 ÷ 3? No!
You can only divide the whole equation by 3 if there’s no separate constant on the x-side.
First get: 3x = 15 (by transposing -2). Then divide: x = 5.
Try These Similar Problems
Problem 1: Solve: 4y + 3 = 19
Transpose +3 → -3: 4y = 19 - 3 = 16 Transpose ×4 → ÷4: y = 16 ÷ 4 = 4
Verify: 4(4) + 3 = 16 + 3 = 19 ✓
Problem 2: Solve: 5n - 10 = 15
Transpose -10 → +10: 5n = 15 + 10 = 25 Transpose ×5 → ÷5: n = 25 ÷ 5 = 5
Verify: 5(5) - 10 = 25 - 10 = 15 ✓
Problem 3: “Three times a number minus 4 equals 17. Find the number.”
Let the number = x. 3x - 4 = 17 3x = 17 + 4 = 21 x = 21 ÷ 3 = 7
The number is 7. Verify: 3(7) - 4 = 21 - 4 = 17 ✓
Exam tip: Two-step equations are the most common type in CBSE Class 7 Chapter 4 exams. For full marks, show each step clearly: (1) the transposition of the constant, (2) the transposition of the coefficient, (3) the final answer, (4) the verification. Four clear steps = full marks.