If 5x-3-5-3x-4x-2- express it as a- x- b- -3- x- 4-3- x- 33- x- -43- x- 4

The correct option is D 3≤ x≤ 4Given: nbsp; nbsp;5x 3 ≤ 5+3x ≤ 4x+2 ⇒ 5x 3 ≤ 5+3x ≤ 4x+2 ⇒ 5x 3 ≤ 5+3x and 5+3x ≤ 4x+2 Rule: If a term of an inequati ...

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Standard X

Mathematics

Shifting Entities

If 5x-3 ≤ 5+3...

Question

If $5 x - 3 \leq 5 + 3 x \leq 4 x + 2$ , express it as $a \leq x \leq b$ .

- 3 \leq x \leq 4

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3 \leq x \leq - 4

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3 \leq x \leq 4

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- 3 \leq x \leq 3

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Solution

The correct option is C $3 \leq x \leq 4$
Given: $5 x - 3 \leq 5 + 3 x \leq 4 x + 2$

$\Rightarrow 5 x - 3 \leq 5 + 3 x \leq 4 x + 2$

$\Rightarrow 5 x - 3 \leq 5 + 3 x and 5 + 3 x \leq 4 x + 2$

Rule: If a term of an inequation is transferred from one side to the other side of the inequation, the sign of the term gets changed. Let's apply this rule in the above inequations.
$\Rightarrow 5 x - 3 x \leq 5 + 3 and 5 - 2 \leq 4 x - 3 x$

$\Rightarrow 2 x \leq 8 a n d 3 \leq x$

$\Rightarrow x \leq 4 a n d x \geq 3$

Therefore,

$a \leq x \leq b \Rightarrow 3 \leq x \leq 4$

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If 5x−3 ≤ 5+3x ≤ 4x+2, express it as a≤x≤b.

If $5 x - 3 \leq 5 + 3 x \leq 4 x + 2$ , express it as $a \leq x \leq b$ .