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Mathematics

Solve 3x5−2x−13>1,x∈R\dfrac{3x}{5} - \dfrac{2x-1}{3} \gt 1, x ∈ \bold{R} and represent the solution set on the number line.

Linear Inequations

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Answer

Given,

3x5−2x−13>1⇒9x−(10x−5)>15⇒9x−10x+5>15⇒−x>15−5⇒−x>10⇒x<−10\dfrac{3x}{5} - \dfrac{2x-1}{3} \gt 1 \\[0.5em] \Rightarrow 9x - (10x - 5) \gt 15 \\[0.5em] \Rightarrow 9x - 10x + 5 \gt 15 \\[0.5em] \Rightarrow - x \gt 15 - 5 \\[0.5em] \Rightarrow - x \gt 10 \\[0.5em] \Rightarrow x \lt -10

x ∈ R.
Hence , Solution set = {x : x ∈ R, x < –10}.

The graph of the solution set is represented by thick black line starting from -10 (not including -10) on the number line.

Solve : (3x/5) - (2x - 1) / 3 > 1, x ∈ R and represent the solution set on the number line. Linear Inequations, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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