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

Question 8

Solve the inequality. 4(x - 3) < x (a) .......................................................... [3] (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 $4(x - 3) < x$ , we start by expanding the left-hand side:

$4x - 12 < x$

Next, we rearrange the inequality by moving all terms involving $x$ to one side and constant terms to the other:

$4x - x < 12$

This simplifies to:

$3x < 12$

Dividing both sides by 3 gives:

$x < 4$

Thus, the solution to the inequality is $x < 4$ .

Step 2

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

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Answer

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

Draw a horizontal line to represent the number line.
Mark the point at 4 with an open circle to indicate that 4 is not included in the solution.
Shade the region to the left of 4 to indicate all numbers less than 4 are included in the solution.

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