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5 (a) Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

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5 (a) Rearrange the equation to make x the subject. y = 7x - 3 (b) Factorise. (i) x² - xy (ii) x² + 8x + 12

Worked Solution & Example Answer:5 (a) Rearrange the equation to make x the subject - OCR - GCSE Maths - Question 5 - 2017 - Paper 1

Step 1

Rearrange the equation to make x the subject.

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Answer

To rearrange the equation y=7x−3y = 7x - 3 to make xx the subject, follow these steps:

  1. Add 3 to both sides: y+3=7xy + 3 = 7x

  2. Divide both sides by 7: x=y+37x = \frac{y + 3}{7}

Thus, the final answer is: x=y+37x = \frac{y + 3}{7}

Step 2

Factorise. (i) x² - xy

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Answer

To factorise the expression x2−xyx² - xy, identify the common factor, which is xx:

x2−xy=x(x−y)x² - xy = x(x - y)

Thus, the final answer is: x(x−y)x(x - y)

Step 3

Factorise. (ii) x² + 8x + 12

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Answer

To factorise the quadratic expression x2+8x+12x² + 8x + 12, look for two numbers that multiply to 12 (the constant term) and add up to 8 (the coefficient of xx). These numbers are 2 and 6.

The factorised form is: x2+8x+12=(x+2)(x+6)x² + 8x + 12 = (x + 2)(x + 6)

Thus, the final answer is: (x+2)(x+6)(x + 2)(x + 6)

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