Solve 2(x + 3) = 14
The Question
Solve: 2(x + 3) = 14
This equation has a bracket, which means we need one extra step before we can solve.
Two Ways to Solve
There are actually two clean methods for this. We’ll cover both.
Method 1: Expand the Brackets First
The distributive law says: a(b + c) = ab + ac.
So: 2(x + 3) = 2 × x + 2 × 3 = 2x + 6
The equation becomes:
2x + 6 = 14
Now solve using transposing:
Step 1: Transpose +6 to the right (becomes -6):
2x = 14 - 6 2x = 8
Step 2: Transpose ×2 to the right (becomes ÷2):
x = 8 ÷ 2 x = 4
Method 2: Divide Both Sides by 2 First
Since both sides of the equation are divisible by 2, we can simplify before expanding.
2(x + 3) = 14
Divide both sides by 2:
(x + 3) = 7
Now transpose +3:
x = 7 - 3 x = 4
Same answer, fewer steps!
When the number outside the bracket divides evenly into the right-hand side, Method 2 is quicker. If it doesn’t divide evenly, use Method 1 (expand first).
Verification
Substitute x = 4 into the original equation: 2(x + 3) = 14
LHS = 2(4 + 3) = 2(7) = 14
RHS = 14
LHS = RHS ✓
x = 4 is correct.
Option A: Expand bracket → ax + b = c → solve in two steps Option B: If RHS is divisible by the bracket coefficient → divide first, then solve
Common mistake: Only multiplying the first term in the bracket.
Wrong: 2(x + 3) = 2x + 3
The 2 must multiply EVERY term inside the bracket. Correct: 2(x + 3) = 2x + 6
This is the most common error in bracket questions!
What If There’s a Minus Sign?
Example: 3(x - 4) = 9
Expanding: 3x - 12 = 9 (the 3 multiplies both x AND -4)
Solving:
3x = 9 + 12 = 21 x = 21 ÷ 3 = 7
Or divide by 3 first:
x - 4 = 3 x = 3 + 4 = 7
The minus sign inside the bracket stays negative after distribution.
Try These Similar Problems
Problem 1: Solve: 3(x + 5) = 21
Method 2 (divide by 3 first, since 21 ÷ 3 = 7): x + 5 = 7 x = 7 - 5 = 2
Verify: 3(2 + 5) = 3(7) = 21 ✓
Problem 2: Solve: 4(2x - 1) = 28
Expand: 8x - 4 = 28 8x = 28 + 4 = 32 x = 32 ÷ 8 = 4
Verify: 4(2×4 - 1) = 4(8 - 1) = 4(7) = 28 ✓
Problem 3: Solve: 5(x + 2) = 3(x + 6)
Expand both sides: 5x + 10 = 3x + 18
Move variable terms to left, constants to right: 5x - 3x = 18 - 10 2x = 8 x = 4
Verify: LHS = 5(4 + 2) = 5(6) = 30. RHS = 3(4 + 6) = 3(10) = 30 ✓
Exam tip: Bracket equations often appear in Class 7 exams as word problems (the perimeter of a rectangle, etc.) where the equation naturally has brackets. Always expand carefully, multiply EVERY term inside, and then solve step by step. Show all working for full marks.