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Linear Inequations — Maths STD 11 Science — Question

Maharashtra 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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