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LINEAR INEQUALITIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLINEAR INEQUALITIES2 Marks
Question
Solve the inequality $\frac{3(x-2)}{5} \leq \frac{5(2-x)}{3}$ for real x.
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Answer

Here $\frac{{3(x - 2)}}{5} \leqslant \frac{{5(2 - x)}}{3}$
$ \Rightarrow \frac{{3x - 6}}{5} \leqslant \frac{{10 - 5x}}{3}$
$ \Rightarrow \frac{{3x}}{5} - \frac{6}{5} \leqslant \frac{{10}}{3} - \frac{{5x}}{3}$
$ \Rightarrow \frac{{3x}}{5} + \frac{{5x}}{3} \leqslant \frac{{10}}{3} + \frac{6}{5}$
$ \Rightarrow \frac{{9x + 25x}}{{15}} \leqslant \frac{{50 + 18}}{{15}}$
$ \Rightarrow \frac{{34x}}{{15}} \leqslant \frac{{68}}{{15}}$
Multiplying both sides by 15, we have
$34x \leqslant 68$
Dividing both sides by 34, we have
$x \leqslant 2$
Thus the solution set is $\left( { - \infty ,2} \right]$

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