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In this question you must show all stages of your working - Edexcel - A-Level Maths Pure - Question 2 - 2022 - Paper 2

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In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 1 shows a sketch of the gr... show full transcript

Worked Solution & Example Answer:In this question you must show all stages of your working - Edexcel - A-Level Maths Pure - Question 2 - 2022 - Paper 2

Step 1

Solve $|3 - 2x| = 7 + x$ for First Case

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Answer

To solve the equation ∣3−2x∣=7+x|3 - 2x| = 7 + x, we need to consider two cases for the absolute value.

Case 1: When 3−2x=7+x3 - 2x = 7 + x:

  1. Rearranging gives:

    3−2x=7+x3 - 2x = 7 + x

  2. Bringing terms involving xx to one side:

    -4 = 3x$$

  3. Dividing both sides by 3:

    x=−43x = -\frac{4}{3}

Step 2

Solve $|3 - 2x| = 7 + x$ for Second Case

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Answer

Case 2: When 3−2x=−(7+x)3 - 2x = -(7 + x):

  1. Expanding gives:

    3−2x=−7−x3 - 2x = -7 - x

  2. Rearranging results in:

    10 = x$$

Thus, we have two solutions: x=−43x = -\frac{4}{3} and x=10x = 10.

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