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Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

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Rearrange the equation to make x the subject. y = 7x - 3 a) x = Factorise. i) x^2 - xy ii) x^2 + 8x + 12

Worked Solution & Example Answer:Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 17 - 2017 - Paper 1

Step 1

Rearrange the equation to make x the subject.

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Answer

To rearrange the equation for y = 7x - 3, we need to isolate x:

  1. Start with the original equation:

    y=7x−3y = 7x - 3

  2. Add 3 to both sides to move the constant term:

    y+3=7xy + 3 = 7x

  3. Divide both sides by 7 to isolate x:

    x=y+37x = \frac{y + 3}{7}

Step 2

Factorise. i) x^2 - xy

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Answer

To factorise the expression x^2 - xy, we can factor out the common term:

  1. Identify the common factor, which is x:

    x2−xy=x(x−y)x^2 - xy = x(x - y)

Step 3

Factorise. ii) x^2 + 8x + 12

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Answer

To factorise the quadratic expression x^2 + 8x + 12, we need to find two numbers that multiply to 12 and add to 8:

  1. The two numbers that satisfy this are 2 and 6.

  2. Therefore, we can write the factorisation as:

    x2+8x+12=(x+2)(x+6)x^2 + 8x + 12 = (x + 2)(x + 6)

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