Guided Lessons

# Solving One-Step Inequalities

This lesson will help students understand how to solve one-step addition, subtraction, multiplication, and division inequalities using inverse operations, as well as how to graph inequalities on a number line.

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Help students understand how to solve one-step addition, subtraction, multiplication, and division inequalities with this seventh-grade lesson plan. Students will learn how to use inverse operations to solve one-step inequalities, while learning some key differences to be aware of when solving multiplication and division inequalities. Students will also gain practice graphing solution sets for inequalities on number lines.

• Students will be able to solve one-step inequalities that involve addition, subtraction, multiplication, and division.
• Students will also be able to graph solution sets for one-step inequalities and interpret solutions within the context of a problem.
(5 minutes)
• Prior to teaching this lesson, make sure that students have practiced solving one-step equations, graphing inequalities on number lines, and operating with positive and negative rational numbers.
• Write the following one-step equations on the whiteboard:
• x + 12 = −4
• y − 8 = 9
• −6m = 72
• b ÷ 4 = −5
• Ask students to solve the one-step equations using inverse operations.
• Ask four students to come up to the board and show how they solved the one-step equations. Make sure students show how to use inverse operations to solve.
(15 minutes)
• Write this one-step inequality on the whiteboard: x + 3 ≥ 11. Ask students to point out what distinguishes inequalities from equations. (Students should note that equations use equal signs and inequalities use symbols like ≥ , ≤, >, and <.)
• State that solving one-step inequalities is similar to solving one-step equations since you can use inverse operations to isolate the variable in both. Note that there are some key differences when solving one-step inequalities, and you will point these out using a few examples.
• Return to the one-step addition inequality you wrote on the whiteboard (x + 3 ≥ 11). Ask students how they would solve this using inverse operations. (Students should say that they would subtract 3 from both sides of the inequality.) Show this step on the whiteboard to get the solution to the inequality (x ≥ 8).
• Remind students that you can graph the solution set to this inequality on a number line. On the whiteboard, write a number line with 8 at the center. Remind students to look at the inequality symbol to determine how to graph the inequality (for x ≥ 8, you should add a closed circle on 8 and shade everything to the right of 8 on the number line).
• Write this one-step subtraction inequality on the board: y − 5 < −1. Have students discuss how to solve this inequality with a partner. Actively monitor student discussions. Then call one student up to the whiteboard to correctly solve this inequality. With the class, talk through how you would graph the solution (y < 4) on a number line (add an open circle on 4 and shade everything to the left of 4).
• Write this one-step multiplication inequality on the board: −3n ≤ 18. Ask students how they would solve this inequality using inverse operations (divide both sides of the inequality by −3). Tell students that any time you divide a multiplication or division inequality by a negative number, you need to flip the inequality sign. So, for this example, the solution is n ≥ −6.
• Provide a brief explanation for why you flip the inequality sign when multiplying or dividing by a negative number. Have students consider the example x > 3. Ask students for one solution to this inequality (e.g., 4 > 3). Tell students that if you multiply both sides of the inequality by −1, the inequality would no longer be true (−4 is not greater than −3). So, you would need to flip the inequality sign to make the inequality true. More generally, any large number will make both x > 3 and −x < −3 true.
• Write this one-step division inequality on the board: g ÷ 2 > −10. Ask students how they would solve this inequality using inverse operations (multiply both sides of the inequality by 2). Point out that since you’re not dividing by a negative number in this example, you don’t need to flip the inequality sign. So, the solution is g > −20.
(15 minutes)
• Hand out the Solving One-Step Inequalities worksheet to students.
• Instruct students to read through the examples on the worksheet as a refresher before they begin working on the practice problems.
• Have each student work with a partner to complete the practice problems. Encourage students to talk through their steps with their partners as they solve and graph the inequalities.
(10 minutes)
• Have students play the Treasure Diving: One-Step Addition and Subtraction Inequalities game and the Treasure Diving: One-Step Multiplication and Division Inequalities game. Students should complete these games independently using a computer (or tablet).

Support:

• If students did not achieve mastery on the one-step inequality games, have them play them again to achieve mastery.
• Instruct students to write down the problems from the games on a piece of paper so they can show all their steps to solve. Ask students to circle any problems that they missed so they can try them again.

Enrichment:

• If students complete the games early, have them work on the One-Step Inequality Word Problems worksheet.
• Students will use computers during independent working time to play the solving one-step inequality games.
(10 minutes)
• Ask students to solve the following one-step inequalities on a sheet of paper. Remind students to show their work as they solve.
• p − 4 < 15
• 5w ≤ −20
• x ÷ (−7) < −3
• j + 9 ≥ −8
• Collect this assessment to gauge student understanding from this lesson.
(5 minutes)
• After you’ve collected the assessment, ask students to turn to a partner and explain how to know if you should flip the inequality sign when solving an inequality. If needed, encourage students to come up with an example problem to explain this.