First, simplify the left-hand side to find that -4*x* + 4 < 2*x* + 3 Then add 4*x* to each side and subtract 3 from each side to find that 1 < 6*x* and finally divide both sides by 6 to find that . We can try a couple of numbers to check that this answer is reasonable. Any value greater than one-sixth should be a solution, so pick a value greater than one-sixth that is easy to work with, like . Okay, can be notoriously *not* easy to work with, but it seems stable enough right now. Now let's see if it satisfies the original inequality. When , the left-hand side of the inequality evaluates to and the right-hand side evaluates to
Because 7 is indeed greater than -2 (if the other team scores a touchdown and you score a negative safety, you are trailing) is a solution to the original inequality. Now let's try one that shouldn't work. Any value less than or equal to one-sixth should not be a solution; pick a value less than one-sixth that is easy to work with, like 0. We hope that 0 will not satisfy the original inequality, but we need to make sure. When *x* = 0, the left-hand side of the inequality evaluates to 4 and the right-hand side evaluates to 3, and 0 is indeed not a solution to the original inequality. While we don't have infinite time to test all possible solutions to the inequality, it is reassuring to check a few values. |