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Question

# Solve each of the following system of equations in R. 8. 5x − 1 < 24, 5x + 1 > −24

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Solution

## $5x-1<24\phantom{\rule{0ex}{0ex}}⇒5x<24+1\phantom{\rule{0ex}{0ex}}⇒x<5\phantom{\rule{0ex}{0ex}}⇒x\in \left(-\infty ,5\right)...\left(\mathrm{i}\right)\phantom{\rule{0ex}{0ex}}\mathrm{Also},5x+1>-24\phantom{\rule{0ex}{0ex}}⇒5x>-24-1\phantom{\rule{0ex}{0ex}}⇒x>-5\phantom{\rule{0ex}{0ex}}⇒x\in \left(-5,\infty \right)...\left(\mathrm{ii}\right)\phantom{\rule{0ex}{0ex}}\mathrm{Hence},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\mathrm{the}\mathrm{intersection}\mathrm{of}\left(\mathrm{i}\right)\mathrm{and}\left(\mathrm{ii}\right).\phantom{\rule{0ex}{0ex}}\left(-\infty ,5\right)\cap \left(-5,\infty \right)=\left(-5,5\right)\phantom{\rule{0ex}{0ex}}\mathrm{Thus},\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{set}\mathrm{of}\mathrm{inequalities}\mathrm{is}\left(-5,5\right).$

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