ICSE Class X Math 2013 Solved Paper

Question : 20 of 46

Marks: +1, -0

SECTION - II

Solve the following inequation, write the solution set and represent it on the number line :

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

Solution:

Given:

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

-\;{x}/{3} ≤ \;{x}/{2}-1 \;{1}/{3}

-\;{x}/{3} ≤ \;{x}/{2}-\;{4}/{3}

\;{4}/{3} ≤ \;{x}/{2}+\;{x}/{3}

\;{4}/{3} ≤ \;{3 x+2 x}/{6}

\;{4}/{3} ≤ \;{5 x}/{6}

\;{6 × 4}/{5 × 3} ≤ x

\;{8}/{5} ≤ x \;\text " or "\; 1.6 ≤ x

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

\;{x}/{2}-\;{4}/{3}\;< \;{1}/{6}

\;{x}/{2}\;< \;{1}/{6}+\;{4}/{3}

\;{x}/{2}\;< \;{1+8}/{6}

\;{x}/{2}\;< \;{9}/{6}

x\;< \;{9 × 2}/{6}

x\;< 3

∴

The solution set is

\{x: 1.6 ≤ x ≤ 3, x ∈ {\R}\}

Number line

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