Find the number of elements which satisfies the given inequalities- -5-2-2 x -4 x -3-4-3-2 x- where- x - whole number-A- 4B- None of theseC- 5D- 3

The correct option is A 4 5/2 +2x ≤ 4x/3≤ 4/3+ 2x 5 +4x/2≤ 4x/3≤ 4+6x/3 [Multiply with 6 throughout] 3( 5 +4x) ≤8x ≤ 2(4 + 6x) 15 + 12x ≤ 8x ≤ 8 +12x 15 + ...

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Byju's Answer

Standard X

Mathematics

Solving Inequalities

Find the numb...

Question

Find the number of elements which satisfies the given inequalities.

$\frac{- 5}{2} + 2 x \leq \frac{4 x}{3} \leq \frac{4}{3} + 2 x$ , where, x $ϵ$ whole number.

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None of these

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Solution

The correct option is B
4

$\frac{- 5}{2} + 2 x \leq \frac{4 x}{3} \leq \frac{4}{3} + 2 x$

$\frac{- 5 + 4 x}{2} \leq \frac{4 x}{3} \leq \frac{4 + 6 x}{3}$ [Multiply with 6 throughout]

$3 (- 5 + 4 x) \leq 8 x \leq 2 (4 + 6 x)$

$- 15 + 12 x \leq 8 x \leq 8 + 12 x$

$- 15 + 12 x \leq 8 x; 8 x \leq 8 + 12 x$

$- 15 \leq - 4 x; - 4 x \leq 8$

$\frac{15}{4} \geq x; x \geq - 2$

So, for satisfying both the inequalities x has {0, 1, 2, 3}. So, 4 elements satisfy the given inequalities.

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Find the number of elements which satisfies the given inequalities. −52+2x≤ 4x3≤ 43+2x, where, x ϵ whole number.

Find the number of elements which satisfies the given inequalities.

$\frac{- 5}{2} + 2 x \leq \frac{4 x}{3} \leq \frac{4}{3} + 2 x$ , where, x $ϵ$ whole number.