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15 (a) Solve - OCR - GCSE Maths - Question 15 - 2020 - Paper 1

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15 (a) Solve. \( \frac{x + 5}{2} = 15 \) (b) Factorise. \( 5a^2 - 10a \) (c) Solve by factorising. \( x^2 + 15x + 56 = 0 \)

Worked Solution & Example Answer:15 (a) Solve - OCR - GCSE Maths - Question 15 - 2020 - Paper 1

Step 1

Solve. \( \frac{x + 5}{2} = 15 \)

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Answer

To solve the equation, first multiply both sides by 2:

x+5=30 x + 5 = 30

Next, subtract 5 from both sides:

x=30−5 x = 30 - 5

Thus, we find:

x=25 x = 25

Step 2

Factorise. \( 5a^2 - 10a \)

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Answer

To factorise the expression, we first notice that both terms share a common factor of 5a. We can factor this out:

5a(a−2) 5a(a - 2)

So, the factorised form is:

5a(a−2) 5a(a - 2)

Step 3

Solve by factorising. \( x^2 + 15x + 56 = 0 \)

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Answer

To solve the quadratic equation by factorising, we need to express it in the form:

(x+m)(x+n)=0 (x + m)(x + n) = 0

where ( m ) and ( n ) are numbers that multiply to 56 and add to 15. The numbers 7 and 8 meet these criteria:

(x+7)(x+8)=0 (x + 7)(x + 8) = 0

Setting each factor to zero gives:

x+7=0→x=−7 x + 7 = 0 \quad \rightarrow \quad x = -7

and

x+8=0→x=−8 x + 8 = 0 \quad \rightarrow \quad x = -8

Thus, the solutions are:

x=−7 or x=−8 x = -7 \text{ or } x = -8

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