If the solution of 20x-4x- 8 and x - 0 is x- k- where k is a variable- then k-

Given: 20x 4x≥ 8 Since the denominator is same(i.e. x), the LCM would be x. ⇒20 4x≥ 8 ⇒16x≥ 8 Since, x gt;0 ∴ Multiplying both sides with x, wont affect th ...

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Standard VII

Mathematics

Solving Inequalities with Unknowns in the Denominator

If the soluti...

Question

If the solution of $\frac{20}{x} - \frac{4}{x} \geq 8$ and $x > 0$ is $x \leq k$ , where $k$ is a variable, then $k =$
2

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Solution

The correct option is A 2
Given: $\frac{20}{x} - \frac{4}{x} \geq 8$
Since the denominator is same(i.e. $x$ ), the LCM would be $x$ .

$\Rightarrow \frac{20 - 4}{x} \geq 8$

$\Rightarrow \frac{16}{x} \geq 8$

Since, $x > 0$
$∴$ Multiplying both sides with $x$ , wont affect the sign of inequality.

$\Rightarrow \frac{16}{x} \times x \geq 8 \times x$
$\Rightarrow 8 x \leq 16$ Or $x \leq 2$
Now, comparing with $x \leq k$
$\Rightarrow k = 2$
We are getting $x$ less than or equal to $2$ . But in the question it was given that $x$ is less than or equal to $k$ .

This implies that the value of $k$ is $2$ .

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If the solution of 20x−4x≥8 and x>0 is x≤k, where k is a variable, then k=2

If the solution of $\frac{20}{x} - \frac{4}{x} \geq 8$ and $x > 0$ is $x \leq k$ , where $k$ is a variable, then $k =$
2