Question

7p+5<=-37 and -10p <10 I need to find the interval notation.

Answer 1

For the given inequalities 7p+5<=-37 and -10p <10 , there is no solution

Given :

7p+5<=-37 and -10p <10

Solve each inequality and find the interval notation

Lets consider first inequality

$7p+5\le \:-37\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\7p\le \:-42\\\mathrm{Divide\:both\:sides\:by\:}7\\p\le \:-6$

Now consider second inequality

$-10p<10\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\10p>-10\\\frac{10p}{10}>\frac{-10}{10}\\p>-1$

$\mathrm{Combine\:the\:intervals}\\p\le \:-6\quad \mathrm{and}\quad \:p>-1$

Both the inequalities does not overlaps

So , No solution

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