The inequality x-3-5 x-2-3-7 x-4-5 holds true for x in the interval

The correct option is C [2,∞)x3≥5x 23 7x 45 x3≥5(5x 2) 3(7x 4)15 5x≥25x 10 21x+12 5x 4x≥ 2 x≥ 2 Thus, all real numbers x which are greater than or equal to 2 , ...

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Standard XII

Mathematics

Manipulation of inequalities

The inequalit...

Question

The inequality $\frac{x}{3} \geq \frac{5 x - 2}{3} - \frac{7 x - 4}{5}$ holds true for $x$ in the interval

(- \infty, 2] \cup [2, \infty)

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[2, \infty)

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(- 2, 2]

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(- \infty, \infty)

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Solution

The correct option is B $[2, \infty)$
$\frac{x}{3} \geq \frac{5 x - 2}{3} - \frac{7 x - 4}{5} \frac{x}{3} \geq \frac{5 (5 x - 2) - 3 (7 x - 4)}{15} 5 x \geq 25 x - 10 - 21 x + 12 5 x - 4 x \geq 2 x \geq 2$
Thus, all real numbers $x$ which are greater than or equal to $2$ , are the solutions of the given inequality.
$∴ x \in [2, \infty)$

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The inequality x3≥5x−23−7x−45 holds true for x in the interval

The correct option is B [2,∞)x3≥5x−23−7x−45x3≥5(5x−2)−3(7x−4)155x≥25x−10−21x+125x−4x≥2x≥2 Thus, all real numbers x which are greater than or equal to 2 , are the solutions of the given inequality. ∴x∈[2,∞)

The inequality $\frac{x}{3} \geq \frac{5 x - 2}{3} - \frac{7 x - 4}{5}$ holds true for $x$ in the interval