In algebra, inequalities are equations in which the answer can be a range of values instead of only one correct solution. For example, 3 plus x is less than 5 is an inequality in which any number under one can be a solution. To teach students in a classroom about solving inequalities, you can use several games and activities to illustrate the concepts.

### Teaching the Symbols

To start teaching inequalities, start by familiarizing students with the symbols and vocabulary of inequalities. Write down the words “less than,” “greater than,” “greater than or equal to” and “less than or equal to” on the board and then write the symbols that correspond to each one. Have the students match the symbols with the wording then define each one by writing an example equation on the board. Have every student write an example so there are plenty of examples for students to reference when they see equations appear on tests and homework.

### Graphs

Give each student a sheet of graph paper and instruct them draw a horizontal line in the center and a vertical line crossing it. The vertical line represents the y-axis and the horizontal line represents the x-axis. Now write down an equation for the students to solve such as “y > x+4.” Have the students select a value for x and then solve for y then plot the point on the graph. Use two other values of x to be able to draw a line on the graph, dotted if you are using greater-or-less-than and solid if you are using greater-than-or-equal-to or less-than-or-equal-to. Have the students shade the left side of the graph if the y is less than the value of x and the right side if y is greater than x. This will teach the students to think visually about inequalities and also chart out solutions for their equations.

### Mystery Game

Pick a number for the value of x and write x=? on the top of a chalk or dry-erase board. Instruct the students how they must solve for x by only asking questions pertaining to inequalities such as, “Is x less than, or equal to, 17?” Any time the answer to their question is “yes,” write the inequality on the board. The first student or team of students to guess the correct value for the variable wins and gets to choose the next value and run the next round. Running a round will help students learn to think quickly about the relationships between numbers in terms of inequalities while guessing will help the students become familiar with the terminology.

### Applications

Apply inequalities to real life to help students understand how equations will work if they come across similar problems. For example, tell students how they must order 50 plates of food but they must spend less than $245 on the order. The students will first need to set up the equation, in this example it would be “50x < 245” where x is the cost of each plate of food. Have the students solve the inequality to learn how much can be spent per plate, in this case x < 4.9 or less than $4.90 per plate. Use this to help students determine how to budget the amount of money someone can spend each week over the course of five weeks and still have money left over.

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