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Linear Inequations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations3 Marks
Question
Solve the following system of equations in R. $\frac{2\text{x}-3}{4}-2\geq\frac{4\text{x}}{3}-6,2(2\text{x}+3)<6(\text{x}-2)+10$
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Answer

Consider the first inequation, $\frac{2\text{x}-3}{4}-2\geq\frac{4\text{x}}{3}-6$ $\frac{2\text{x}-3-8}{4}\geq\frac{4\text{x}-18}{3}$ $3(2\text{x}-11)\geq4(4\text{x}-18)$ $6\text{x}-33\geq16\text{x}-72$ $6\text{x}-16\text{x}\geq-72+33$ $-10\text{x}\geq-39$ $\text{x}\leq\frac{39}{10}\ ...(\text{i})$ Consider the second inequation, 2 (2x + 3) < 6 (x - 2) + 10 4x + 6 < 6x - 12 + 10 4x - 6x < -12 - 6 + 10 -2x < -8 x > 8 ..(ii) From (i) and (ii), There is no solution set of the simultaneous equations.

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