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Mathematics

List the solution set of the inequation

12+8x>5x−32,x∈Z\dfrac{1}{2} + 8x \gt 5x -\dfrac{3}{2}, x ∈ \bold{Z}

Linear Inequations

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Answer

Given, 12+8x>5x−32⇒8x−5x>−32−12⇒3x>−42⇒3x>−2⇒x>−23\dfrac{1}{2} +8x \gt 5x - \dfrac{3}{2} \\[0.5em] \Rightarrow 8x-5x \gt - \dfrac{3}{2}-\dfrac{1}{2} \\[0.5em] \Rightarrow 3x \gt - \dfrac{4}{2} \\[0.5em] \Rightarrow 3x \gt -2 \\[0.5em] \Rightarrow x \gt -\dfrac{2}{3}

Since , x ∈ Z
Solution set = {0, 1, 2, 3, 4…..}

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