5x/2+3x/4≥39/4 ⇒10x+3x/4≥39/4 ⇒ 13x ≥ 39 ⇒ x ≥39/13=3 ⇒ x≥ 3 ∴ The solution set is [3,∞ ] ...

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Properties of Inequalities

5 x/2+3 x/4≥3...

Question

$\frac{5 x}{2} + \frac{3 x}{4} \geq \frac{39}{4}$

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Solution

$\frac{5 x}{2} + \frac{3 x}{4} \geq \frac{39}{4} \Rightarrow \frac{10 x + 3 x}{4} \geq \frac{39}{4} \Rightarrow 13 x \geq 39 \Rightarrow x \geq \frac{39}{13} = 3 \Rightarrow x \geq 3 ∴ T h e s o l u t i o n s e t i s [3, \infty]$

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