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Mathematics

Solve the following inequation.

11+3x5≥3−x>−32\dfrac{11 + 3x}{5} \ge 3 - x \gt -\dfrac{3}{2}, x ∈ R

(a) Write the solution set.

(b) Represent the solution on the number line.

Linear Inequations

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Answer

Given,

11+3x5≥3−x>−32\dfrac{11 + 3x}{5} \ge 3 - x \gt -\dfrac{3}{2}

Solving L.H.S. of the equation,

⇒11+3x5≥3−x⇒11+3x≥5(3−x)⇒11+3x≥15−5x⇒3x+5x≥15−11⇒8x≥4⇒x≥48⇒x≥12 ………..(1)\Rightarrow \dfrac{11 + 3x}{5} \ge 3 - x \\[1em] \Rightarrow 11 + 3x \ge 5(3 - x) \\[1em] \Rightarrow 11 + 3x \ge 15 - 5x \\[1em] \Rightarrow 3x + 5x \ge 15 - 11 \\[1em] \Rightarrow 8x \ge 4 \\[1em] \Rightarrow x \ge \dfrac{4}{8} \\[1em] \Rightarrow x \ge \dfrac{1}{2} \text{ ………..(1)}

Solving R.H.S. of the equation,

⇒3−x>−32⇒x<3+32⇒x<6+32⇒x<92 …….(2)\Rightarrow 3 - x \gt -\dfrac{3}{2} \\[1em] \Rightarrow x \lt 3 + \dfrac{3}{2} \\[1em] \Rightarrow x \lt \dfrac{6 + 3}{2} \\[1em] \Rightarrow x \lt \dfrac{9}{2} \text{ …….(2)}

From equation (1) and (2), we get :

⇒12≤x<92\Rightarrow \dfrac{1}{2} \le x \lt \dfrac{9}{2}

Solve the following inequation. Maths Competency Focused Practice Questions Class 10 Solutions.

Hence, solution set = {x:12≤x<92,x∈Rx : \dfrac{1}{2} \le x \lt \dfrac{9}{2}, x ∈ R}

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