# Problem Solving Involving Inequalities The rules for solving inequalities are similar to those for solving linear equations. • Solving One-Step Linear Inequalities in One Variable The solutions to linear inequalities can be expressed several ways: using inequalities, using a graph, or using interval notation.However, there is one exception when multiplying or dividing by a negative number. The steps to solve linear inequalities are the same as linear equations, except if you multiply or divide by a negative when solving for the variable, you must reverse the inequality symbol. Express the solution as an inequality, graph and interval notation.To solve an inequality, we can: • Add the same number to both sides.

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Solving real-world problems that involve inequalities is very much like solving problems that involve equations.

In order to get a bonus this month, Leon must sell at least 120 newspaper subscriptions.

We solve the inequality by dividing both sides by 4.50: x ≥ 144.44. What must the length be if the perimeter is at least 180 inches? The formula for perimeter is: Perimeter = 2 x length 2 x width Since the perimeter must be at least 180 inches, we have 2x 2(20) ≥ 180.

We round up the answer to 145 since only whole boxes can be sold. Check If we multiply 145 by \$4.50 we obtain \$652.50, so if Virenas troop sells more than 145 boxes they will raise more than \$650.

I've tried to provide you with examples that could pertain to your life and come in handy one day.

Think about others ways you might use inequalities in real world problems. Before we look at the examples let's go over some of the rules and key words for solving word problems in Algebra (or any math class).Because by moving the smaller term, I was able to avoid having a negative coefficient on the variable, and therefore I was able to avoid having to remember to flip the inequality when I divided off that coefficient.I find it simpler to work this way; I make fewer errors. Why did I switch the inequality in the last line and put the variable on the left?Solution Let x = the number of subscriptions Leon sells in the last week of the month.The total number of subscriptions for the month must be greater than 120, so we write : 85 x ≥ 120.If he sells 35 or more subscriptions, the total number of subscriptions he sells that month will be 120 or more. Virenas Scout troop is trying to raise at least 0 this spring.How many boxes of cookies must they sell at .50 per box in order to reach their goal? Then the inequality describing this problem is 4.50 ≥ 650.Note that, since I had to divide through by a negative, I had to flip the inequality signs.Note also that you might (as I do) find the above answer to be more easily understood if written the other way around: Always remember when doing word problems, that, once you've found the value for the variable, you need to go back and re-read the problem to make sure that you're answering the actual question.But if they sell 144 boxes, they will only raise 8, which is not enough. The procedure for solving linear inequalities in one variable is similar to solving basic equations.

## Comments Problem Solving Involving Inequalities

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