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Gemma’s solution to the inequality $3x + 1 > -5$ is shown on the number line - OCR - GCSE Maths - Question 2 - 2018 - Paper 1

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Gemma’s solution to the inequality $3x + 1 > -5$ is shown on the number line. Is Gemma’s solution correct? Explain your reasoning.

Worked Solution & Example Answer:Gemma’s solution to the inequality $3x + 1 > -5$ is shown on the number line - OCR - GCSE Maths - Question 2 - 2018 - Paper 1

Step 1

Determine the correct inequality solution

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Answer

To solve the inequality 3x+1>−53x + 1 > -5, we first isolate xx:

  1. Subtract 1 from both sides:
    3x>−63x > -6

  2. Divide both sides by 3:
    x>−2x > -2

This means the solution should be represented as x>−2x > -2.

Step 2

Examine the number line representation

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Answer

We need to check if Gemma's number line shows the correct placement.

For the solution x>−2x > -2, the number line should have an open circle at -2, indicating that -2 is not included, and the shading should extend to the right, indicating all numbers greater than -2.

Step 3

Conclude whether Gemma's solution is correct

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Answer

If Gemma’s number line shows an open circle at -2 with an arrow pointing to the right, her solution is correct. However, if it shows an arrow pointing in the wrong direction or a closed circle at -2, then her solution is incorrect.

In conclusion, evaluate the number line:

  • If the open circle is placed at -2 and the arrow points right, then Gemma's solution is correct.
  • Otherwise, she has made an error.

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