Find the value of x, which satisfy the inequation -2 \frac{5}{6}< \frac{1}{2}-\frac{2 x}{3} \leq 2, x \in W. Graph the solution set on the number line.

ICSE Class X Math 2014 Solved Paper - Question 2

Question : 2 of 52

Marks: +1, -0

Find the value of

x

, which satisfy the inequation

-2 \;{5}/{6}< \;{1}/{2}-\;{2 x}/{3} ≤ 2, x ∈ W

. Graph the solution set on the number line.

Solution:

Given:

-2 \;{5}/{6}< \;{1}/{2}-\;{2 x}/{3} ≤ 2

⇒ \;\; -\;{17}/{6} < \;{3-4 x}/{6} ≤ 2

Multiplying throughout by 6

\;-17 < 3-4 x ≤ 12

\;-17 < 3-4 x \;\text " and "\; 3-4 x ≤ 12

\;⇒ \;\; 4 x < 3+17 \;\text " and "\; 3-12 ≤ 4 x

\;⇒ \;\; 4 x < 20 \;\text " and "\;-9 ≤ 4 x

\;⇒ \;\; x < 5 \;\text " and "\;-\;{9}/{4}< x

\; \{5>x ≥ \;{-9}/{4}\}

Hence, the solution set is

\{x: x ∈ {\W},-\;{9}/{4} ≤ x < 5\}

∴

Values of

x

are

\{0,1,2,3,4\}

The graph of the solution set is shown by dots on the number line.

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