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LINEAR INEQUALITIES — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLINEAR INEQUALITIES2 Marks
Question
Solve the inequality $\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}$ for real x.
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Answer

Here $\frac{x}{4} < \frac{{(5x - 2)}}{3} - \frac{{(7x - 3)}}{5}$
$ \Rightarrow \frac{x}{4} < \frac{{5x}}{3} - \frac{2}{3} - \frac{{7x}}{5} + \frac{3}{5}$ $ \Rightarrow \frac{{15x - 100x + 84x}}{{60}} < \frac{{ - 10 + 9}}{{15}}$
$ \Rightarrow \frac{{ - x}}{{60}} < \frac{{ - 1}}{{15}}$
Multiplying both sides by 60, we have
-x < -4
Dividing both sides by -1, we have
x > 4
Thus the solution set is $(4,\infty )$

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