Linear Inequations — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations3 Marks
Question
Solve the following system of equations in R. $\frac{|\text{x}-2|}{\text{x}-2}>0$
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Answer
We have $\frac{|\text{x}-2|}{\text{x}-2}>0\ ...(\text{i})$ Case1: when $|\text{x}-2|\geq0$ $\text{x}\geq2$ $\Rightarrow\frac{\text{x}-2}{\text{x}-2}\geq0$ $\Rightarrow\text{x}-2\geq0$ $\text{x}\geq2\ ..(\text{ii})$ Case 2: When |x - 2| < 0 x < 2 $\Rightarrow-\frac{(\text{x}-2)}{\text{x}-2}>0$ ⇒ -(x - 2) > 0 ⇒ -x + 2 < 0 ⇒ x < -2 ⇒ x > 2 ...(iii) Combining (ii) and (iii), we get $(2,\infty)$ as the solution set.
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