Question 119119
Let's solve the first inequality:



{{{-5<4x+7}}} Start with the given inequality




{{{0<4x+7+5}}}Add 5 to both sides



{{{-4x<7+5}}} Subtract 4x from both sides



{{{-4x<12}}} Combine like terms on the right side



{{{x>(12)/(-4)}}} Divide both sides by -4 to isolate x  (note: Remember, dividing both sides by a negative number flips the inequality sign) 




{{{x>-3}}} Divide


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Answer:

So our answer is {{{x>-3}}} 




Now let's solve the second inequality:





{{{5x-6<14}}} Start with the given inequality




{{{5x<14+6}}}Add 6 to both sides



{{{5x<20}}} Combine like terms on the right side



{{{x<(20)/(5)}}} Divide both sides by 5 to isolate x 




{{{x<4}}} Divide


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Answer:

So our answer is {{{x<4}}} 




So we have the answers:


{{{x>-3}}} and {{{x<4}}}



which forms the compound inequality:


{{{-3<x<4}}} 



So our answer is {{{-3<x<4}}}