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7. (a) Solve - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Question 7

7. (a) Solve. (i) 4x = 56 (ii) \frac{126}{x} = 7 (iii) 8x - 6 = 46 (b) Solve by factorising. x^2 + 11x + 30 = 0

Worked Solution & Example Answer:7. (a) Solve - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Step 1

(i) 4x = 56

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Answer

To solve for x, divide both sides by 4:

$x = \frac{56}{4} = 14$

Step 2

(ii) \frac{126}{x} = 7

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Answer

To solve for x, cross-multiply:

$126 = 7x$

Next, divide both sides by 7:

$x = \frac{126}{7} = 18$

Step 3

(iii) 8x - 6 = 46

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Answer

To isolate x, add 6 to both sides:

$8x = 46 + 6$

Which simplifies to:

$8x = 52$

Now, divide both sides by 8:

$x = \frac{52}{8} = 6.5$

Step 4

Solve by factorising. x^2 + 11x + 30 = 0

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Answer

To solve the quadratic equation by factorising, we need to find two numbers that multiply to 30 and add to 11. The numbers are 5 and 6:

$(x + 5)(x + 6) = 0$

Setting each factor to zero gives:

$x + 5 = 0 \Rightarrow x = -5$
$x + 6 = 0 \Rightarrow x = -6$

Thus, the solutions are:

$x = -5 \text{ or } x = -6$

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