Number of integral solutions of 2 x -1- x -7- 0 isA- 7B- infiniteC- 6D - 5

The correct option is C 62x 1x 7≤0 (i) 2x − 1 ≤ 0 and x − 7 0 x ≤12 and x 7 not possible (ii) 2x − 1 ≥ 0 and x − 7 0 x ≥12 and x 7 nbsp; ⇒ x∈[12,7) Numbe ...

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Standard XII

Mathematics

Method of Intervals

Number of int...

Question

Number of integral solutions of $\frac{2 x - 1}{x - 7} \leq 0$ is

5

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6

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7

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infinite

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Solution

The correct option is B $6$
$\frac{2 x - 1}{x - 7} \leq 0$
$(i)$
$2 x - 1 \leq 0$ and $x - 7 > 0$
$x \leq \frac{1}{2}$ and $x > 7$ not possible

$(i i)$
$2 x - 1 \geq 0$ and $x - 7 < 0$
$x \geq \frac{1}{2}$ and $x < 7$
$\Rightarrow x \in [\frac{1}{2}, 7)$

Number of integral solution is $1, 2, 3, 4, 5, 6$

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Number of integral solutions of 2x−1x−7≤0 is

The correct option is B 62x−1x−7≤0 (i) 2x−1≤0 and x−7>0 x≤12 and x>7 not possible (ii) 2x−1≥0 and x−7<0 x≥12 and x<7 ⇒x∈[12,7) Number of integral solution is 1,2,3,4,5,6

Number of integral solutions of $\frac{2 x - 1}{x - 7} \leq 0$ is