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# 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.

No standards associated with this content.

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• Students will be able to solve one-step inequalities that involve addition, subtraction, multiplication, and division.
• 学生还将能够在问题的背景下为一步不平等的解决方案集合设置并解释解决方案。
(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分钟）
• 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.
• 返回您在白板上写的一步添加不等式（x +3≥11）。询问学生如何使用反操作来解决此问题（学生应该说他们将从不平等的两侧减去3）。在白板上显示此步骤，以获取不等式的解决方案（x≥8）。
• 提醒学生，您可以在数字行上将解决方案设置为此不等式。在白板上，在中心写下一个数字线。提醒学生查看不等式符号以确定如何绘制不等式（对于x≥8，您应该在8上添加一个封闭的圆圈，并在数字行上的8个右侧遮荫）。
• 在董事会上写下此一步减法不平等：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.
• 简要说明为什么在乘以或除以负数时将不平等标志翻转。让学生考虑示例x> 3.向学生询问一种解决这种不平等的解决方案（例如4> 3）。告诉学生，如果您将不平等的两面乘以-1，则不平等将不再是正确的（-4不大于-3）。因此，您需要翻转不平等标志，以使不平等现实。更一般而言，任何大数量都会使x> 3和-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分钟）
• 向学生分发解决一步不平等的工作表。
• Instruct students to read through the examples on the worksheet as a refresher before they begin working on the practice problems.
• 让每个学生与伴侣一起工作以完成练习问题。鼓励学生在解决和绘制不平等现象时与伴侣进行措施。
(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).

• 如果学生没有在单步不平等游戏上精通掌握，请再次玩他们以实现精通。
• 指示学生在一张纸上写下游戏中的问题，以便他们显示所有解决步骤。要求学生圈出他们错过的任何问题，以便他们可以再次尝试。

• If students complete the games early, have them work on the One-Step Inequality Word Problems worksheet.
• 学生将在独立工作时间内使用计算机来播放解决单步不平等游戏。
(10 minutes)
• 要求学生在一张纸上解决以下一步不平等。提醒学生在解决时展示自己的工作。
• 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.

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