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

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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 of the equation by 4:

x=564=14x = \frac{56}{4} = 14

Step 2

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

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Answer

To isolate x, multiply both sides by x:

126=7x126 = 7x

Now divide both sides by 7:

x=1267=18x = \frac{126}{7} = 18

Step 3

(iii) 8x - 6 = 46

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Answer

First, add 6 to both sides:

8x=46+68x = 46 + 6

This simplifies to:

8x=528x = 52

Now, divide both sides by 8:

x=528=6.5x = \frac{52}{8} = 6.5

Step 4

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

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Answer

To factor the quadratic, we look for two numbers that multiply to 30 and add to 11. The numbers 5 and 6 work:

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

Setting each factor to zero gives:

  1. ( x + 5 = 0 \Rightarrow x = -5 )
  2. ( x + 6 = 0 \Rightarrow x = -6 )

Thus, the solutions are:

x=−5 or x=−6x = -5 \text{ or } x = -6

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