First slide

Introduction to linear inequalities

Question

The values of x which satisfy the inequalities simultaneously
$(i) - 3 < 2 x - 1 < 19$
$(ii) - 1 \leq \frac{2 x + 3}{5} \leq 3$

Moderate

A

$[- 4, 10)$
B

$(- 1, 6]$
C

$[- 1, 6)$
D

$(- 1, 6)$

Solution

$- 3 < 2 x - 1 < 19 \Rightarrow - 2 < 2 x < 20 \Rightarrow - 1 < x < 10 - - - - - (1)$
$- 1 \leq \frac{2 x + 3}{5} \leq 3 \Rightarrow - 5 \leq 2 x + 3 \leq 15 \Rightarrow - 8 \leq 2 x \leq 12$
$\Rightarrow - 4 \leq x \leq 6 - - - - - (2)$
$Now from (1) and (2) common values are (- 1, 6] .$

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