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Complete this identity by writing in the missing numbers - OCR - GCSE Maths - Question 16 - 2023 - Paper 2

Question 16

Complete this identity by writing in the missing numbers. 4(.....x + 1) = 14x - 6(x - 2) - ...

Worked Solution & Example Answer:Complete this identity by writing in the missing numbers - OCR - GCSE Maths - Question 16 - 2023 - Paper 2

Step 1

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Answer

To solve for the missing numbers, we start by expanding the expression on the left:

$4(.....x + 1) = 4(.....x) + 4(1) = 4(.....x) + 4$

Next, we consider the right-hand side, which is given as:

$14x - 6(x - 2)$

Expanding this:

$14x - 6x + 12 = 8x + 12$

Thus, we need to match the left side with the right side.

Step 2

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Answer

From the earlier calculation, we determined that:

$4(.....x + 1) = 8x + 12$

To make these equal, we set the coefficients of x equal to each other:

ightarrow ..... = 2$$ Now, substituting back we have: 4(2x + 1) Finally, comparing the constant terms: $$4$$ on the left should equal $$12 - ...$$ on the right. We find: $$12 - ... = 4 ightarrow ... = 8$$. Thus the answer for the missing numbers is: $$4(2x + 1) = 14x - 6(x - 2) - 8$$.

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