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ICSE Class X Math 2013 Paper

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Question : 20 of 46
Marks: +1, -0
SECTION - II
Solve the following inequation, write the solution set and represent it on the number line :
−x3≤x2−113<16,x∈R-\frac{x}{3} \le \frac{x}{2} - 1\frac{1}{3} < \frac{1}{6}, x \in R
Solution:  
Given: −x3≤x2−113<16-\frac{x}{3} \le \frac{x}{2} - 1\frac{1}{3} < \frac{1}{6}
−x3≤x2−113-\frac{x}{3} \le \frac{x}{2} - 1\frac{1}{3}
−x3≤x2−43-\frac{x}{3} \le \frac{x}{2} - \frac{4}{3}
43≤x2+x3\frac{4}{3} \le \frac{x}{2} + \frac{x}{3}
43≤3x+2x6\frac{4}{3} \le \frac{3x+2x}{6}
43≤5x6\frac{4}{3} \le \frac{5x}{6}
6×45×3≤x\frac{6 \times 4}{5 \times 3} \le x
85≤x or 1.6≤x\frac{8}{5} \le x \text{ or } 1.6 \le x
x2−113<16\frac{x}{2} - 1\frac{1}{3} < \frac{1}{6}
x2−43<16\frac{x}{2} - \frac{4}{3} < \frac{1}{6}
x2<16+43\frac{x}{2} < \frac{1}{6} + \frac{4}{3}
x2<1+86\frac{x}{2} < \frac{1+8}{6}
x2<96\frac{x}{2} < \frac{9}{6}
x<9×26x < \frac{9 \times 2}{6}
x<3x < 3
∴\therefore The solution set is {x:1.6≤x≤3,x∈R}\{x: 1.6 \le x \le 3, x \in R\} Number line
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