Rearranging formulae Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Rearranging formulae questions. See exactly how to solve problems on changing the subject, inverse operations, negative terms, science formula.

changing the subjectinverse operationsnegative termsscience formulaspeed formulaarea formula
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Make xx the subject of y=x+8y = x + 8.

Worked solution

  1. Write down the formula

    y=x+8y = x + 8

    Make xx the subject, starting from the given formula.

  2. Subtract 8 from both sides

    y−8=xy - 8 = x

    The inverse of +8+8 is −8-8; do it to both sides to keep the balance.

  3. State the answer

    x=y−8x = y - 8

    Now xx is the subject.

Answer
x=y−8x = y - 8
Question 2
1 markeasy
Make xx the subject of y=x−3y = x - 3.

Worked solution

  1. Write down the formula

    y=x−3y = x - 3

    Make xx the subject.

  2. Add 3 to both sides

    y+3=xy + 3 = x

    The inverse of −3-3 is +3+3.

  3. State the answer

    x=y+3x = y + 3

    Now xx is the subject.

Answer
x=y+3x = y + 3
Question 3
1 markeasy
Make xx the subject of y=5xy = 5x.

Worked solution

  1. Write down the formula

    y=5xy = 5x

    Make xx the subject.

  2. Divide both sides by 5

    y5=x\frac{y}{5} = x

    The inverse of ×5\times 5 is ÷5\div 5.

  3. State the answer

    x=y5x = \frac{y}{5}

    Now xx is the subject.

Answer
x=y5x = \frac{y}{5}
Question 4
1 markeasy
Make xx the subject of y=x4y = \frac{x}{4}.

Worked solution

  1. Write down the formula

    y=x4y = \frac{x}{4}

    Make xx the subject.

  2. Multiply both sides by 4

    4y=x4y = x

    The inverse of ÷4\div 4 is ×4\times 4.

  3. State the answer

    x=4yx = 4y

    Now xx is the subject.

Answer
x=4yx = 4y
Question 5
1 markeasy
Make aa the subject of c=a+bc = a + b.

Worked solution

  1. Write down the formula

    c=a+bc = a + b

    Make aa the subject.

  2. Subtract b from both sides

    c−b=ac - b = a

    The inverse of +b+b is −b-b.

  3. State the answer

    a=c−ba = c - b

    Now aa is the subject.

Answer
a=c−ba = c - b

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