Question 253680


{{{x+8>=-7x+8>7}}} Start with the given compound inequality.



Break up the compound inequality to get:



{{{x+8>=-7x+8}}} AND {{{-7x+8>7}}}



So let's solve the first inequality {{{x+8>=-7x+8}}}



{{{x+8>=-7x+8}}} Start with the given inequality.



{{{x>=-7x+8-8}}} Subtract {{{8}}} from both sides.



{{{x+7x>=8-8}}} Add {{{7x}}} to both sides.



{{{8x>=8-8}}} Combine like terms on the left side.



{{{8x>=0}}} Combine like terms on the right side.



{{{x>=(0)/(8)}}} Divide both sides by {{{8}}} to isolate {{{x}}}. 



{{{x>=0}}} Reduce.



Now let's solve the second inequality {{{-7x+8>7}}}



{{{-7x+8>7}}} Start with the given inequality.



{{{-7x>7-8}}} Subtract {{{8}}} from both sides.



{{{-7x>-1}}} Combine like terms on the right side.



{{{x<(-1)/(-7)}}} Divide both sides by {{{-7}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<1/7}}} Reduce.


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Answer:


So the solution is {{{x>=0}}} <b>and</b> {{{x<1/7}}}.



Our answer also looks like {{{0<=x<1/7}}}.