First, simplify the left-hand side: -4*x* + 4 < 2*x* + 3 Then add 4*x* to each side and subtract 3 from each side: 1 < 6*x* And finally divide both sides by 6: 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's easy to work with, like 1. It doesn't get much easier than 1. Now let's see if it satisfies the original inequality. When *x* = 1, here's what our original inequality turns into: -4(1 – 1) < 2(1) + 3 -4(0) < 2 + 3 0 < 5 Because 0 is indeed less than 5 (if the other team scores 5 points and you score nothing, you're trailing), we can tell *x* = 1 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's easy to work with, like 0. We hope that 0 won't satisfy the original inequality, but we need to make sure. When *x* = 0, here's what we get: -4(0 – 1) < 2(0) + 3 -4(-1) < 0 + 3 4 < 3 That's not true: 4 ain't smaller than 3. Which is totally what we wanted, 'cause that means 0 is *not* a solution. While we don't have infinite time to test all possible solutions to the inequality, it's reassuring to check a few values. |