If the replacement set is the set of all non-negative integers, find the solution set of the following
A) $x + 1 < 9$
B) $3 x - 4 ⩽ 20$
C) $5 + 2 x > 10$
D) $10 < x + 5 < 21$

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Solution

A. $x + 1 < 9$

$x < 9 - 1 \Rightarrow x < 8$

$x \in [0, 7]$

B. $3 x - 4 \leq 20$

$3 x \leq 24 \Rightarrow x \leq 8$

$x \in [0, 8]$

C. $5 + 2 x > 10$

$2 x > 5$

$x > \frac{5}{2}, x \in [3, \infty]$

D. $10 < x + 5 < 21$

$5 < x < 16$

$x \in [6, 15]$

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