AlgebraHigherAlgebraRearranging FormulaeChanging the Subject
AQA GCSE · Question 16 · Algebra
Rearrange y = √( (x/2) + 1 ) to make x the subject.
How to approach this question
1. The aim is to isolate x on one side of the equation.
2. Start by eliminating the square root. Do the inverse operation, which is squaring, to both sides of the equation.
3. Next, isolate the term containing x (which is x/2). Do the inverse of adding 1, which is subtracting 1, from both sides.
4. Finally, isolate x completely. Do the inverse of dividing by 2, which is multiplying by 2, to both sides.
Full Answer
We are asked to rearrange the formula y = √( (x/2) + 1 ) to make x the subject. This means we need to perform a series of inverse operations to get x by itself.
Original formula:
y = √( (x/2) + 1 )
Step 1: Eliminate the square root.
The inverse operation of taking a square root is squaring. We must square both sides of the equation.
y² = (√( (x/2) + 1 ))²
y² = (x/2) + 1
Step 2: Isolate the term with x.
The term with x is being added to 1. The inverse is to subtract 1 from both sides.
y² - 1 = (x/2) + 1 - 1
y² - 1 = x/2
Step 3: Isolate x.
x is being divided by 2. The inverse is to multiply by 2 on both sides.
2 * (y² - 1) = (x/2) * 2
2(y² - 1) = x
So, the final rearranged formula is x = 2(y² - 1). This can also be written as x = 2y² - 2.
Common mistakes
✗ Squaring the terms inside the square root individually, e.g., y² = x²/4 + 1. This is incorrect.
✗ Multiplying by 2 before subtracting 1. The order of operations is crucial.
✗ Forgetting to apply the operation to both sides of the equation.
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