If -2 x-5-3- then x -

The correct option is C [52,7)For √(2x 5) lt;3 to be defined 2x 5≥ 0 ⇒2x≥ 5⇒ x≥52 nbsp; Squaring both the sides, We get nbsp; 2x 5 lt;9⇒2x lt;14⇒ x ...

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Standard XII

Mathematics

Method of Intervals

If √2 x-5<3, ...

Question

If $\sqrt{2 x - 5} < 3$ , then $x \in$

(\frac{5}{2}, \infty)

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[\frac{5}{2}, \infty)

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[\frac{5}{2}, 7)

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(- \infty, 7)

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Solution

The correct option is C $[\frac{5}{2}, 7)$
For $\sqrt{2 x - 5} < 3$ to be defined
$2 x - 5 \geq 0 \Rightarrow 2 x \geq 5 \Rightarrow x \geq \frac{5}{2}$

Squaring both the sides, We get
$2 x - 5 < 9 \Rightarrow 2 x < 14 \Rightarrow x < 7$

Taking intersection of both the conditions, we get
$x \in [\frac{5}{2}, 7)$

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If √2x−5<3, then x∈

The correct option is C [52,7)For √2x−5<3 to be defined 2x−5≥0⇒2x≥5⇒x≥52 Squaring both the sides, We get 2x−5<9⇒2x<14⇒x<7 Taking intersection of both the conditions, we get x∈[52,7)

If $\sqrt{2 x - 5} < 3$ , then $x \in$