ICSE Class X Math 2016 Solved Paper

Question : 8 of 57

Marks: +1, -0

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

-3(x-7) ≥ 15-7 x>\;{x+1}/{3}, x ∈ R

Solution:

Given :

-3(x-7) ≥ 15-7 x>\;{x+1}/{3}

\;-3 x+21 ≥ 15-7 x>\;{x+1}/{3}

\;⇒-3 x+21 ≥ 15-7 x

and

15-7 x>\;{x+1}/{3}

\;⇒ \;\; 4 x ≥-6

and

45-21 x>x+1

\;⇒ \;\; x ≥-\;{3}/{2} \;\text " and "\; 44>22 x

\;⇒ \;\; x ≥ \;{-3}/{2} \;\text " and "\; \;\; 2>x

∴ Solution set

= \{x: x ∈ {\R}, \;{-3}/{2} ≤ x< 2\}

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