First mistake

1. Question

Solve 3(x − 2) + 5 = 20.

Show all working.

2. Result

Multiply everything inside the brackets

The first mistake is on the line that rewrites 3(x − 2). Demo mark 1/4. Demo estimate, not an official CXC mark.

CSEC topic: Expanding brackets using the distributive law.

4. Why it is incorrect

Multiply everything inside the brackets

You multiplied 3 by x, but you also need to multiply 3 by −2.

3(x − 2) = 3x − 6

The later lines followed on from that new equation. That is why 17/3 appears: it is one missed multiplication, not a second independent mistake. CSEC: follow-through — later working that continues from an earlier slip.

1. Step 1

   3(x − 2) + 5 = 20

   Start with the original equation

2. Step 2

   3x − 6 + 5 = 20

   Multiply 3 by both x and −2

3. Step 3

   3x − 1 = 20

   Combine −6 and +5

4. Step 4

   3x = 21

   Add 1 to both sides

5. Step 5

   x = 7

   Divide both sides by 3

Check: 3(7 − 2) + 5 = 3 × 5 + 5 = 15 + 5 = 20

6. What you understood

The rest of the working followed on

• The original equation was copied correctly.
• You started by taking the brackets out. That was the right first move.
• You combined the numbers after that. CSEC: collect like terms — add or subtract the parts that are the same kind.
• You undid the operations in a clear order to find x. CSEC: inverse operations — do the opposite; isolate the variable — get the letter on its own.