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Solve :

−15≤3x10+1<25-\dfrac{1}{5} \le \dfrac{3x}{10} + 1 \lt \dfrac{2}{5}, x ∈ R. Graph the solution set on the number line.

Linear Inequations

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Answer

Given,

Equation :

−15≤3x10+1<25-\dfrac{1}{5} \le \dfrac{3x}{10} + 1 \lt \dfrac{2}{5}

Solving L.H.S. of the above inequation :

⇒−15≤3x10+1⇒3x10≥−15−1⇒3x10≥−1−55⇒3x10≥−65⇒x≥−65×103⇒x≥−4 ………(1)\Rightarrow -\dfrac{1}{5} \le \dfrac{3x}{10} + 1 \\[1em] \Rightarrow \dfrac{3x}{10} \ge -\dfrac{1}{5} - 1 \\[1em] \Rightarrow \dfrac{3x}{10} \ge \dfrac{-1 - 5}{5} \\[1em] \Rightarrow \dfrac{3x}{10} \ge -\dfrac{6}{5} \\[1em] \Rightarrow x \ge -\dfrac{6}{5} \times \dfrac{10}{3} \\[1em] \Rightarrow x \ge -4 \text{ ………(1)}

Solving R.H.S. of the above inequation :

⇒3x10+1<25⇒3x10<25−1⇒3x10<2−55⇒3x10<−35⇒x<−35×103⇒x<−2 ………(2)\Rightarrow \dfrac{3x}{10} + 1 \lt \dfrac{2}{5} \\[1em] \Rightarrow \dfrac{3x}{10} \lt \dfrac{2}{5} - 1 \\[1em] \Rightarrow \dfrac{3x}{10} \lt \dfrac{2 - 5}{5} \\[1em] \Rightarrow \dfrac{3x}{10} \lt -\dfrac{3}{5} \\[1em] \Rightarrow x \lt -\dfrac{3}{5} \times \dfrac{10}{3} \\[1em] \Rightarrow x \lt -2 \text{ ………(2)}

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

Solve. -1/5 ≤ 3x/10 + 1 < 2/5, x ∈ R. Graph the solution set on the number line. Model Paper 2, Concise Mathematics Solutions ICSE Class 10.

Solution set : {x : x ∈ R and -4 ≤ x < -2}.

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