2.3A: Harder Rearranging (The Factoriser)
When the subject appears TWICE or is wrapped in layers
5x - 5 = 3x + 2
Original equation
The Logic Track
⚠️ THE TRAP
If x appears on BOTH sides, you CANNOT just divide!
✓ THE STRATEGY
1
GROUP all x terms on one side
EXAMINER TIP:
Notice how 3x becomes -3x when moved to the left. This is the "Change Side, Change Sign" rule.
The Rearranging Engine
Make
x the subject of:
y = (3x + 1)/(x - 4)
STEP 1: Multiply both sides by (x - 4)
y(x - 4) = 3x + 1
STEP 2: Expand brackets
xy - 4y = 3x + 1
STEP 3: Group x terms on left
xy - 3x = 1 + 4y
STEP 4: Factorise x
x(y - 3) = 1 + 4y
STEP 5: Divide both sides by (y - 3)
x = (1 + 4y)/(y - 3)