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7 (a) Show the inequality $x > 3$ on this number line - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

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7 (a) Show the inequality $x > 3$ on this number line. (b) Simplify, $$4a + 3c + 7a - 5c.$$ (c) Solve.

Worked Solution & Example Answer:7 (a) Show the inequality $x > 3$ on this number line - OCR - GCSE Maths - Question 7 - 2018 - Paper 1

Step 1

Show the inequality $x > 3$ on this number line.

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Answer

To represent the inequality x>3x > 3 on the number line:

  1. Draw a hollow circle at 3 to indicate that 3 is not included in the solution.
  2. Shade the region to the right of 3 to represent all values greater than 3.

Step 2

Simplify, $4a + 3c + 7a - 5c$.

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Answer

Combine like terms:

  1. Combine the terms with 'a': 4a+7a=11a.4a + 7a = 11a.
  2. Combine the terms with 'c': 3c−5c=−2c.3c - 5c = -2c.

Thus, the simplified expression is:

11a−2c.11a - 2c.

Step 3

Solve.

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Answer

Let's assume a simple equation such as: 2x+12=0.2x + 12 = 0.

  1. To isolate x, first subtract 12 from both sides: 2x=−12.2x = -12.
  2. Then, divide by 2: x=−6.x = -6.

If the equation differs, please adjust the values accordingly. The process remains the same.

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