A number is doubled, then decreased by $13.7$.  The result is greater than $125.28$. What is the smallest integer that satisfies this condition?
I need to find the smallest integer x that satisfies the inequality 2x - 13.7 > 125.28. I can rearrange this inequality by adding 13.7 to both sides, getting 2x > 138.98. Then I can divide both sides by 2, getting x > 69.49. The smallest integer that is greater than 69.49 is 70, so that is the answer. 