Use real number line to find the range of values of x for which :

(i) $x > 3 a n d 0 < x < 6.$

(ii) $x < 0 a n d - 3 \leq x < 1.$

(iii) $- 1 < x \leq 6 a n d - 2 \leq x \leq 3$

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Solution

(i) x > 3 and 0 < x < 6
Both the given inequations are true in the range where their graphs on the real number lines overlap.
The graphs of the given inequations can be drawn as:

From both graphs, it is clear that their common range is
3 < x < 6

(ii) x < 0 and -3 ≤ x < 1
Both the given inequations are true in the range where their graphs on the real number lines overlap.
The graphs of the given inequations can be drawn as:

From both graphs, it is clear that their common range is
-3 ≤ x < 0

(iii) -1 < x ≤ 6 and -2 ≤ x ≤ 3
Both the given inequations are true in the range where their graphs on the real number lines overlap.
The graphs of the given inequations can be drawn as:

From both graphs, it is clear that their common range is
-1 < x ≤ 3

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