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Solve the inequality - OCR - GCSE Maths - Question 8 - 2021 - Paper 1

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Question 8

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Solve the inequality. 4(x - 3) < x (a) ............................................................... (b) Show your answer to part (a) on the number line.

Worked Solution & Example Answer:Solve the inequality - OCR - GCSE Maths - Question 8 - 2021 - Paper 1

Step 1

Solve the inequality.

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Answer

To solve the inequality, we start by distributing the 4 on the left side:

4(x3)<x4(x - 3) < x

This expands to:

4x12<x4x - 12 < x

Next, we will isolate x by subtracting x from both sides:

4xx12<04x - x - 12 < 0

This simplifies to:

3x12<03x - 12 < 0

Now, we will add 12 to both sides:

3x<123x < 12

Next, we divide by 3:

x<4x < 4

Thus, the solution to the inequality is:

Answer: x<4x < 4.

Step 2

Show your answer to part (a) on the number line.

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Answer

To represent the solution x<4x < 4 on a number line:

  • Draw a number line ranging from -6 to 6.
  • Place an open circle on 4 to indicate that 4 is not included in the solution.
  • Shade the region to the left of 4 to show that the values are less than 4.

This visually indicates all the numbers that are less than 4.

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