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Vyacheslav Rybakov
Vyacheslav Rybakov

Two-step inequalities: What are they and how to solve and write them?


Lesson 7 Homework Practice Solve and Write Two Step Inequalities Answers




If you are struggling with solving and writing two step inequalities, you are not alone. Many students find this topic challenging and confusing. But don't worry, we are here to help you. In this article, we will explain what two step inequalities are, how to solve them, and how to write the answers correctly. We will also provide you with some examples and practice problems that you can use for your homework.




lesson 7 homework practice solve and write two step inequalities answers



What are Two Step Inequalities?




An inequality is a mathematical statement that compares two expressions using one of these symbols: , , or . For example, 3x + 5


A two step inequality is an inequality that requires two steps to solve. For example, 2x - 4 > 10 is a two step inequality because you need to add 4 to both sides and then divide by 2 to find the value of x.


The solution of a two step inequality is a range of values that make the inequality true. For example, the solution of 2x - 4 > 10 is x > 7, which means that any number greater than 7 makes the inequality true.


How to Solve Two Step Inequalities?




To solve a two step inequality, you need to follow these steps:


  • Isolate the variable term on one side of the inequality by adding or subtracting the constant term from both sides.



  • Divide or multiply both sides of the inequality by the coefficient of the variable term to get the value of the variable.



  • If you multiply or divide by a negative number, reverse the direction of the inequality symbol.



  • Write the solution as an inequality using the variable and the symbol.



For example, let's solve this two step inequality: 5x + 3 -22


  • Subtract 3 from both sides: 5x -25



  • Divide both sides by 5: x -5



  • The direction of the inequality symbol does not change because we divided by a positive number.



  • The solution is x -5



How to Write Two Step Inequalities Answers?




To write two step inequalities answers, you need to follow these rules:


  • Use the same variable and symbol as in the original inequality.



  • Use parentheses around the variable term if it has more than one term or if it has a negative coefficient.



  • Use a comma to separate multiple solutions or use the word "or" to indicate alternative solutions.



  • Use brackets [ ] to indicate that an endpoint is included in the solution or use parentheses ( ) to indicate that an endpoint is excluded from the solution.



  • Use interval notation or set notation to write the solution as a set of values.



For example, let's write the answer for this two step inequality: -3x + 6


  • The variable and symbol are x and <.



  • We use parentheses around (-3x) because it has a negative coefficient.



  • We have only one solution, so we do not need a comma or "or".



  • We use parentheses ( ) around -5 because it is excluded from the solution.



  • We can write the solution as (-, -5) using interval notation or as x < -5 using set notation.



Examples and Practice Problems




To help you understand and practice solving and writing two step inequalities better, here are some examples and practice problems that you can try. You can check your answers using Khan Academy or IXL websites.


Example 1: Solve and write the answer for this two step inequality: 4x - 8 12


  • Add 8 to both sides: 4x 20



  • Divide both sides by 4: x 5



  • The direction of the inequality symbol does not change because we divided by a positive number.



  • The answer is x 5



Example 2: Solve and write the answer for this two step inequality: -2x + 5 > -11


  • Subtract 5 from both sides: -2x > -16



  • Divide both sides by -2: x < 8



  • The direction of the inequality symbol changes because we divided by a negative number.



  • The answer is x < 8



Practice Problem 1: Solve and write the answer for this two step inequality: x/3 + 2 -1


How to Check Your Answers for Two Step Inequalities?




After you solve and write the answer for a two step inequality, you should always check your answer to make sure it is correct. To check your answer, you need to follow these steps:


  • Pick any value from the solution set and plug it into the original inequality.



  • Simplify both sides of the inequality using the order of operations.



  • Compare both sides of the inequality using the inequality symbol.



  • If the inequality is true, then your answer is correct. If the inequality is false, then your answer is incorrect.



For example, let's check our answer for this two step inequality: x/3 + 2 -1


  • We solved this inequality and got x -9 as the answer. Let's pick -10 from the solution set and plug it into the original inequality.



  • We get (-10)/3 + 2 -1. Simplifying both sides, we get -10/3 + 6/3 -3/3, which is -4/3 -3/3.



  • Comparing both sides, we see that -4/3 is indeed less than or equal to -3/3, so the inequality is true.



  • Since the inequality is true, our answer is correct.



How to Practice Solving and Writing Two Step Inequalities?




The best way to practice solving and writing two step inequalities is to do lots of problems and check your answers. You can find many online resources that offer practice problems and solutions for two step inequalities. Some of these resources are:


  • Khan Academy: This website offers interactive lessons, videos, quizzes, and exercises on various math topics, including two step inequalities. You can learn at your own pace and track your progress.



  • IXL: This website offers adaptive practice problems on various math skills, including two step inequalities. You can get immediate feedback and explanations for your answers.



  • TPT: This website offers various teaching resources created by teachers for teachers, including activities, worksheets, games, and projects on two step inequalities. You can download and print these resources for your homework or classroom use.



Conclusion




In this article, we have explained what two step inequalities are, how to solve them, and how to write the answers correctly. We have also provided you with some examples and practice problems that you can use for your homework. We hope this article has helped you understand and practice solving and writing two step inequalities better.


How to Graph Two Step Inequalities?




Another way to represent the solution of a two step inequality is to graph it on a number line. To graph a two step inequality, you need to follow these steps:


  • Solve the inequality and write the answer using the variable and the symbol.



  • Draw a number line and mark the value of the variable that makes the inequality an equation. This is called the boundary point.



  • Use a closed circle [ ] if the boundary point is included in the solution or an open circle ( ) if the boundary point is excluded from the solution.



  • Shade the part of the number line that contains the values that make the inequality true. Use an arrow to indicate that the shading continues indefinitely.



For example, let's graph this two step inequality: 3x - 6


  • We solved this inequality and got x < 5 as the answer.



  • We draw a number line and mark 5 as the boundary point.



  • We use an open circle ( ) around 5 because it is excluded from the solution.



  • We shade the part of the number line that is less than 5 and use an arrow to indicate that it goes on forever.



How to Solve Word Problems with Two Step Inequalities?




Sometimes, you may encounter word problems that involve two step inequalities. To solve word problems with two step inequalities, you need to follow these steps:


  • Read and understand the problem carefully. Identify what is given and what is asked.



  • Define a variable to represent the unknown quantity in the problem.



  • Write an inequality that models the situation in the problem using the variable and the given information.



  • Solve the inequality and write the answer using the variable and the symbol.



  • Interpret the answer in terms of the problem and write it in a complete sentence.



For example, let's solve this word problem with a two step inequality:


Amy wants to buy a new laptop that costs $800. She has saved $200 so far and she earns $15 per hour at her part-time job. How many hours does she need to work at her job to have enough money to buy


How to Graph Two Step Inequalities?




Another way to represent the solution of a two step inequality is to graph it on a number line. To graph a two step inequality, you need to follow these steps:


  • Solve the inequality and write the answer using the variable and the symbol.



  • Draw a number line and mark the value of the variable that makes the inequality an equation. This is called the boundary point.



  • Use a closed circle [ ] if the boundary point is included in the solution or an open circle ( ) if the boundary point is excluded from the solution.



  • Shade the part of the number line that contains the values that make the inequality true. Use an arrow to indicate that the shading continues indefinitely.



For example, let's graph this two step inequality: 3x - 6


  • We solved this inequality and got x < 5 as the answer.



  • We draw a number line and mark 5 as the boundary point.



  • We use an open circle ( ) around 5 because it is excluded from the solution.



  • We shade the part of the number line that is less than 5 and use an arrow to indicate that it goes on forever.



How to Solve Word Problems with Two Step Inequalities?




Sometimes, you may encounter word problems that involve two step inequalities. To solve word problems with two step inequalities, you need to follow these steps:


  • Read and understand the problem carefully. Identify what is given and what is asked.



  • Define a variable to represent the unknown quantity in the problem.



  • Write an inequality that models the situation in the problem using the variable and the given information.



  • Solve the inequality and write the answer using the variable and the symbol.



  • Interpret the answer in terms of the problem and write it in a complete sentence.



For example, let's solve this word problem with a two step inequality:


Amy wants to buy a new laptop that costs $800. She has saved $200 so far and she earns $15 per hour at her part-time job. How many hours does she need to work at her job to have enough money to buy 4e3182286b


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