If 5-2 x -3- x -6-5- then x lies inB- -8- -C- -8- -D- - 8-

The correct option is C [8,∞)(5 2x3)×6≤( x6 5)×6 nbsp; (∵ multiplication with positive number won’t affect inequality) ⇒ 10 – 4x ≤ x – 30 ⇒ 5x ≥ 40 ⇒ x ≥ 8 ...

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Standard XII

Mathematics

Different Types of Intervals in Inequality

If 5-2 x /3≤ ...

Question

If $\frac{5 - 2 x}{3} \leq \frac{x}{6} - 5$ , then $x$ lies in

[8, \infty)

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(- \infty, 8]

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(- \infty, - 8]

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[- 8, \infty)

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Solution

The correct option is A $[8, \infty)$
$(\frac{5 - 2 x}{3}) \times 6 \leq (\frac{x}{6} - 5) \times 6$
( $∵$ multiplication with positive number won’t affect inequality)
$\Rightarrow 10 - 4 x \leq x - 30$
$\Rightarrow 5 x \geq 40$
$\Rightarrow x \geq 8$

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Similar questions

If $\frac{4 x + 8}{5 x + 8} = \frac{5}{6}$ , then x = ?

(a) 4

(b) 6

(d) 12

Q. If

| | 2 x - x^{2} + 8 | - | x^{2} + 5 | | = | 2 x + 13 |

, then

x

lies in

Q. If

| | 2 x - x^{2} + 8 | - | x^{2} + 5 | | = | 2 x + 13 |

, then

x

lies in

Let f(x) = $| x - 3 |$ + $| x - 5 |$

Then f(x) = 2x - 8 if x $\geq$ 5

= 8 - 2x if x $\leq$ 3

Q. If

\frac{1}{3} x + 5 = 8

, then x = ?
(a) 3
(b) 6
(c) 9
(d) 12

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If 5−2x3≤x6−5, then x lies in

The correct option is A [8,∞)(5−2x3)×6≤(x6−5)×6 (∵ multiplication with positive number won’t affect inequality) ⇒10–4x≤x–30 ⇒5x≥40 ⇒x≥8

If $\frac{5 - 2 x}{3} \leq \frac{x}{6} - 5$ , then $x$ lies in

The correct option is A $[8, \infty)$
$(\frac{5 - 2 x}{3}) \times 6 \leq (\frac{x}{6} - 5) \times 6$
( $∵$ multiplication with positive number won’t affect inequality)
$\Rightarrow 10 - 4 x \leq x - 30$
$\Rightarrow 5 x \geq 40$
$\Rightarrow x \geq 8$