Question 198548
{{{10^(x+3)>100^(x-1)}}} Start with the given inequality.



{{{10^(x+3)>(10^2)^(x-1)}}} Rewrite 100 as {{{10^2}}}



{{{10^(x+3)>10^(2(x-1))}}} Multiply the exponents.



{{{x+3>2(x-1)}}} Since the bases are equal, this means that the right exponent MUST be larger than the left exponent.



{{{x+3>2x-2}}} Distribute.



{{{x>2x-2-3}}} Subtract {{{3}}} from both sides.



{{{x-2x>-2-3}}} Subtract {{{2x}}} from both sides.



{{{-x>-2-3}}} Combine like terms on the left side.



{{{-x>-5}}} Combine like terms on the right side.



{{{x<(-5)/(-1)}}} Divide both sides by {{{-1}}} to isolate {{{x}}}. note: Remember, the inequality sign flips when we divide both sides by a negative number. 



{{{x<5}}} Reduce.



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Answer:


So the solution is {{{x<5}}}