$-5≤\frac{5-3x}{2}≤8$

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Target Exam

CUET

Subject

-- Applied Mathematics - Section B2

Chapter

Numbers, Quantification and Numerical Applications

Question:

$-5≤\frac{5-3x}{2}≤8$

Options:

$\left[\frac{-11}{3}, 5\right]$

$\left[\frac{-13}{3}, 5\right]$

$\left[\frac{-10}{3}, 3\right]$

$\left[\frac{-11}{2}, 3\right]$

Correct Answer:

$\left[\frac{-11}{3}, 5\right]$

Explanation:

The correct answer is option (1) : $\left[\frac{-11}{3}, 5\right]$

$-5≤\frac{5-3x}{2}≤8$

$-10≤5-3x≤16$

$-10-5≤-3x≤16-5$

$-15≤-3x≤11$

$-15≤-3x$

$-3x≥-15$

$x≤5$

and

$-3x≤11$

$3x≥-11$

$x≥\frac{-11}{3}$

$\frac{-11}{3}≤x≤5$

∴ Solution set is { x : x ∈ R, $\frac{-11}{3}≤x≤5$}i.e $\left[\frac{-11}{3}, 5\right]$