CAIE IGCSE Mathematics Extended E2.6 Inequalities Question Bank

Practise reading, solving and graphing inequalities, from number lines and integer solutions to regions bounded by straight lines.

Exam points

read compound inequalities from number lines and list the integer values that satisfy them
solve linear inequalities from algebra or calculator-cost contexts, preserving the inequality sign
draw boundary lines and shade unwanted regions to label the feasible region R

[Maximum number: 6]

(a)

Write down the inequality shown by the number line.

[ 1 ]

$-2<x\leqslant4$ oe

(b)

$-3\leqslant2x+3<9$

[ 5 ]

(i)

Solve the inequality.

[ 3 ]

$-3\leqslant x<3$ final answer
M2 for correct intermediate inequality; SC1 for one side correct

(ii)

Write down all the integer values of x that satisfy the inequality.

[ 2 ]

[Maximum number: 2]

Solve.

6 x+14>6

$x>-\frac43$ or $x>-1\frac13$ final answer
M1 for 6x>6-14 or $x+\frac{14}{6}>1$

[Maximum number: 1]

Region R satisfies the three inequalities $y \geqslant 0, y \leqslant x$ and $x+y \geqslant 7$ . On the grid, label the region R .

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