Solve 8-3 x-3-2 x-3-4

The correct option is C [4,∞)8 3x3≤2x3 4 ⇒ 8 3x ≤ 2x 12 ⇒ 5x≥ 20⇒ x≥ 4 Thus, all real numbers x which are greater than or equal to 4 are the solutions of the g ...

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Standard XII

Mathematics

Properties of absolute inequality

Solve 8-3 x/3...

Question

Solve $\frac{8 - 3 x}{3} \leq \frac{2 x}{3} - 4$

[2, \infty)

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[4, \infty)

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[5, \infty)

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(- \infty, \infty)

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Solution

The correct option is B $[4, \infty)$
$\frac{8 - 3 x}{3} \leq \frac{2 x}{3} - 4 \Rightarrow 8 - 3 x \leq 2 x - 12 \Rightarrow 5 x \geq 20 \Rightarrow x \geq 4$
Thus, all real numbers $x$ which are greater than or equal to $4$ are the solutions of the given inequality, i.e., $x \in [4, \infty) .$

Suggest Corrections

Solve 8−3x3≤2x3−4

The correct option is B [4,∞)8−3x3≤2x3−4⇒8−3x≤2x−12⇒5x≥20⇒x≥4 Thus, all real numbers x which are greater than or equal to 4 are the solutions of the given inequality, i.e., x∈[4,∞).

Solve $\frac{8 - 3 x}{3} \leq \frac{2 x}{3} - 4$

The correct option is B $[4, \infty)$
$\frac{8 - 3 x}{3} \leq \frac{2 x}{3} - 4 \Rightarrow 8 - 3 x \leq 2 x - 12 \Rightarrow 5 x \geq 20 \Rightarrow x \geq 4$
Thus, all real numbers $x$ which are greater than or equal to $4$ are the solutions of the given inequality, i.e., $x \in [4, \infty) .$