 # Solve Multi-Step Word Problems (Inequalities)

Related Topics:
Common Core for Mathematics
Lesson Plans and Worksheets for all Grades

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

B. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where pq, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

Common Core: 7.EE.4b

### Suggested Learning Targets

• I can solve simple inequalities.
• I can solve two step linear inequalities of the form px+ q > r and px+q < r, where p, q, and r are specific rational numbers.
• I can solve word problems (two-step linear inequality problems) with rational coefficients (ex, px +q = r).
• I can graph the solution sets of inequalities.
• I can interpret the solution sets of the inequality.
Solving Inequalities by Adding or Subtracting When you add or subtract the same number from each side of an inequality, the inequality remains true.
Examples:
1. Solve -21 ≥ d - 8. Check your solution.
2. Solve y + 5 > 11. Check your solution.
3. Kayla took \$12 to the bowling alley. Shoe rental costs \$3.75. What is the most he could spend on games and snacks?
Solving Inequalities Using Addition and Subtraction
Examples:
Solve and graph the solutions.
1. t + 3 < 10
2. x - 2.2 ≥ 6.8
3. 5 > 7 + V

### Solve Inequalities with Multiplication and Division

When you multiply or divide by a negative, the inequality symbol must flip

Solving Inequalities by Multiplying and Dividing

### Solve 2-Step Inequalities

Solving 2-step inequalities
How to solve and graph 2-step inequalities? Solving Two - Step Linear Inequalities
Here we solve a few inequalities that require addition / subtraction and multiplication / division. Solving Two-Step Inequalities

### Inequality Word Problems

How to Translate Word Problems Into Multistep Inequalities?
In this lesson, we'll go over some word problems, which, in order to find their solution, require us to translate them into (multi-step) inequalities -- inequalities which take more than one step to solve. Writing An Inequality From A Word Problem
The elevator of a local school has a maximum weight capacity of 2,000 pounds. If there are already 3 people on the elevator that have a combined weight of 460 pounds, write an inequality expressing the possible weights that may be added to the elevator. Use "w" to represent the weight. Example:
When John bought his new computer, he purchased an online computer help service. The help service has a yearly fee of \$25.50 and a \$10.50 charge for each help session a person uses. If John can only spend \$170 for the computer help this year, what is the maximum number of help sessions he can use this year?

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 