Linear Inequations — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLinear Inequations1 Mark
Question
Write the solution set of the inequation |2 - x| = x - 2.
✓
Answer
|2 - x| = x - 2 ...(i)
$2-\text{x}\geq0$ for $\text{x}\leq2$
⇒ |2 - x| = 2 - x
2 - x < 0 for x > 2
⇒ |2 - x|= - (2 - x)
for x > 2 from (i)
|2 - x| = x - 2
⇒ x = 2
Which is not true as x < 2 and x = 2 cannot happen at same time.
For $\text{x}\geq2$ from (i)
|2 - x| = -(2 - x)
From (i)
$\therefore$ -(2 - x) = x - 2x
⇒ x - 2x = x - 2x which is not true.
Hence the solution on set of the given inequation is $(2,\infty)$
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