INEQUALITIES
Solve inequalities as you would any other equation. Isolate the variable for which you are solving on one side of the equation and
everything else on the other side of the equation.The only difference here is that instead of finding a specific value for a, you get a range of values for a. The rest of the math is the
same.There is, however, one crucial difference between solving equations and inequalities. When you multiply or divide an inquality by
a negative number, you must change the direction of the sign.If this seems confusing, think about the logic. You’re told that −5 times something is greater than 10. This is where your knowledge
of positives and negatives comes into play. You know that negative × positive = negative and negative × negative = positive. Since
−5 is negative and 10 is positive, −5 has to be multiplied by something negative to get a positive product. Therefore a has to be less
than −2, not greater than it. If a > −2, then any value for a that is greater than −2 should make −5a greater than 10. Say a is 20, −5a
would be −100, which is certainly not greater than 10.The point here is that, while it’s a good idea to memorize that you need to flip the sign if you multiply or divide by a negative, the
math makes sense if you think about it.Exercise
xii. Solve for y in each of the following inequalities.
y + 2 > 10
10 +2a − 3 < 4 − a
6 y < −20 + y
18 − 6y > 12
3(y + 10) − 4 > 2 + 5(2y − 3)