Solve an inequality much like an equation.Simplify down each side and then get the variable by itself by doing the opposite operation to all sides. The one thing different is that when you multiply or divide by a NEGATIVE number you must switch the inequality sign.
Now we will solve 2 inequalities at the same time and combine their answers into one final statement. Solve each individual problem as in section 1. We can combine the answers in one of 2 methods.
Conjuction (and) We want the answers that fit ALL parts.
Disjuntion (or) We want the answers that fit ANY parts.
Just like chapter 1, make sure the problem you set up is what the words are telling you. At least is the same as greater than or equal to and at most is less than or equal to. Don't forget to check your answer to make sure its the right format and that you have answered the question in the problem and not just solved the inequality you created. Correct format means integer answer when talking about how many people, etc. If greater than always round up regardless if the fraction part is greater than one half or not. Less than always round down.
Going back to the definition of absolute value from chapter 1, there are two possible numbers that give a certain value. We don't know if we are dealing with the positive or negative case, so we must do both cases. For case 1, just drop the absolute value bars and the rest of the problem stays the same. For case 2, drop the absolute value, change the inequality sign and take the opposite of the other side of the inequality. Make sure the absolute value is by itself before setting up the 2 cases. Basically treat the absolute value as a new variable and get it by itself then follow the above rules to get your 2 cases.
example: |2x-3| + 3 < 6 subtract 3 from both sides to get |2x-3| < 3 and then set up your 2 cases which would be
2x-3 < 3 and 2x-3 > -3