Solving inequalities is very similar to solving equations.
Solving Inequalities Practice Problem: x + 5 ≥ -3
Use the inverse operation to isolate the variable by - 5 on both sides
x ≥ -8
The inequality has been solved. If asked for possible solutions, you must say that the answer could be any number equal to or greater than -8. Pay attention to the inequality symbols as they tell you exactly which numbers can be solutions.
The main difference to note between solving inequalities and solving equations is that when dividing or multiplying by a negative number (when you have a negative coefficient for your variable), you must flip the inequality symbol to its opposite to keep the inequality true. See the videos below for examples.
Practice Problems in Class:
(1) The product of nine and x is greater than six more than the product of three and x.
(2) Mrs. Scott decided that she would spend no more than $120 to buy a jacket and a skirt. If the price of the jacket was $20 more than 3 times the price of the skirt. Find the highest possible price of the skirt?
(3) Stephanie weighs 3 times as much as Rachel. Both weights are whole numbers and the sum of their weights is less than 160 pounds. Find the greatest possible weight for each girl.
(4) Six more than two times a certain number is less than the number increased by twenty. Find the numbers that satisfy this condition.
(5) Two consecutive even integers are such that their sum is greater than 98 decreased by twice the larger. Find the smallest possible values for the integers.
(6) Mrs. Smith wrote "Eight less than three times a number is greater than fifteen" on the board. If x represents the number, write an inequality that is a correct translation of this statement.
The documents below are handouts for practice problems (not all problems to be completed) reviewed in class as classwork or homework. Notes are provided in class to add to the handouts or the journal entries.