SOLUTION: solve: 10^x+3>100^x-1

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Question 198548: solve:
10^x+3>100^x-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
10%5E%28x%2B3%29%3E100%5E%28x-1%29 Start with the given inequality.


10%5E%28x%2B3%29%3E%2810%5E2%29%5E%28x-1%29 Rewrite 100 as 10%5E2


10%5E%28x%2B3%29%3E10%5E%282%28x-1%29%29 Multiply the exponents.


x%2B3%3E2%28x-1%29 Since the bases are equal, this means that the right exponent MUST be larger than the left exponent.


x%2B3%3E2x-2 Distribute.


x%3E2x-2-3 Subtract 3 from both sides.


x-2x%3E-2-3 Subtract 2x from both sides.


-x%3E-2-3 Combine like terms on the left side.


-x%3E-5 Combine like terms on the right side.


x%3C%28-5%29%2F%28-1%29 Divide both sides by -1 to isolate x. note: Remember, the inequality sign flips when we divide both sides by a negative number.


x%3C5 Reduce.


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Answer:

So the solution is x%3C5