Finding Inequalities from Regions (Edexcel IGCSE Maths A (Modular))

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Always read the question carefully to see if the diagram shades the wanted region or the unwanted region.

Write down the three inequalities which define the shaded region shown on the axes below.

Find the equations of the three lines shown (ignoring inequality signs for now)

You may be able to see the lines $x = 1$ and $y = x$
The other line has the form $y = m x + c$ with y-intercept 7 and gradient -1

Now decide which inequality signs to use

For $y = x$ , the shaded region is above the line, and the line is dotted, so the inequality is

$y > x$

If unsure, check by substituting in coordinates from the shaded region
For example, using (2, 4) as marked on the graph above

" $4 > 2$ " is true, so the inequality $y > x$ is correct

For $y = - x + 7$ , the shaded region is below the line, and the line is solid, so the inequality is

$y \leq - x + 7$

Again, check by substituting (2, 4) into the inequality

" $4 \leq - 2 + 7$ " is true, so the inequality $y \leq - x + 7$ is correct

For $x = 1$ , the shaded region is to the right of the solid line so the inequality is

$x \geq 1$

Write all three inequalities together as your final answer

$y > x$ , $y \leq - x + 7$ and $x \geq 1$

the (exam) results speak for themselves:

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