The region R is shown on this grid. Region R is defined by four inequalities. One of the inequalities is $x \geq 0$. Use the symbols to complete the other three inequalities. $x \geq 0$ $y \ldots \frac{1}{2}x$ $x + 2y \ldots 24$ $y \ldots x + 6$ The inequality $x > 0$ is replaced by a new inequality. Region R is then a kite. Write down the new inequality.

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The region R is shown on this grid - OCR - GCSE Maths - Question 12 - 2021 - Paper 1

Question 12

The region R is shown on this grid. Region R is defined by four inequalities. One of the inequalities is $x \geq 0$. Use the symbols < and > to complete the other ... show full transcript

Worked Solution & Example Answer:The region R is shown on this grid - OCR - GCSE Maths - Question 12 - 2021 - Paper 1

Step 1

$y \ldots \frac{1}{2}x$

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Answer

To find the inequality, note that the line $y = \frac{1}{2}x$ intersects the region R. Since region R is below this line, we use the inequality $y < \frac{1}{2}x$ .

Step 2

$x + 2y \ldots 24$

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Answer

The line $x + 2y = 24$ indicates a boundary for region R. To determine the inequality, we observe that the region is below this line, hence we write $x + 2y \leq 24$ .

Step 3

$y \ldots x + 6$

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Answer

The line $y = x + 6$ forms a boundary above region R. Thus, we express this inequality as $y < x + 6$ .

Step 4

Write down the new inequality.

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Answer

The new inequality that replaces $x > 0$ and makes region R a kite is $x \geq 0$ .

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