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Inequality Word Problems Worksheets

We use inequalities to compare two values. They give us an idea of relative size by stating that one is greater, lesser, equal, or not equal to the other value. Many times, when we use math, we do not need an exact answer, just an idea if something is going to work. I was reminded of this concept this very morning. I am a lacrosse coach and I have a bag that carries 80 lacrosse balls. There were already 28 balls in the bag and the school bought me a 50 pack of new balls. I had to quickly understand if that entire pack would fit in my bag. With the help of a quick inequality, I figured out there were too many for the bag. These worksheets and lessons help students learn how to write inequalities when given a word problem.

Aligned Standard: Grade 7 Expression & Equations - 7.EE.B.4b

  • Amanda and Her Flowers Step-by-step Lesson- How many lilies can she afford? She wants to buy a pair of red rose flowers for $18 and spend the rest on lily flowers. Each lily flower costs $11. Write an inequality for the number of lily flowers she can purchase.
  • Guided Lesson - Kimberly has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality for the number of school shoes she can purchase.
  • Guided Lesson Explanation - Pay close attention to the graphing explanation it will save you time and time again.
  • Practice Worksheet - This one may take students a lot time. Make sure to give them plenty of time and scrap paper.
  • Matching Worksheet - If you are really good at writing and understanding inequalities, this will be a breeze for you.
  • Applied Problems of Inequalities Five Worksheet Pack - I totally love these types of problems. Most people will call them riddles when they are just really calculated math.
  • Triangular Inequalities Worksheet Five Pack - It is all about finding the longest side based on the measure of angles.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

We start students off with the word problems and then we move to number lines.

  • Homework 1 - Jacob gives his son $30 for chocolate. His son spends $16 on dark chocolate and spends the rest on white chocolate. Each white chocolate costs $7. Write an inequality for the number of white chocolate he can purchase.
  • Homework 2 - Solve -0.3x – 4 > -9.4 and graph the solution on a number line.
  • Homework 3 - Sarah has $80. She wants to purchase a school bag for $16 and as many pairs of shoes as she can. Each pair of shoes is $8. Write an inequality to find how many pairs of shoes she can purchase.

Practice Worksheets

The biggest problem here is for students to remember the difference between an open and closed inline arrow.

  • Practice 1 - Solve 2x + 2 > 4 and graph the solution on a number line.
  • Practice 2 - Brock has $23 to spend on cupcakes. He wants to buy an orange cupcake for $8 and spend the rest on pink cupcakes. Each pink cupcake costs $5. Write an inequality that can be used to determine the number of pink cupcakes Brock can buy.
  • Practice 3 - Mary has $20 to spend. She buys lunch for $14 and spends the rest on banana biscuits. Each banana biscuit costs $3. How many banana biscuits did she buy?

Math Skill Quizzes

I couldn't fit any number line based questions in here, sorry!

  • Quiz 1 - Margaret wants to purchase a caramel apple ($7) and water melon slice ($4). She spends the rest of her money on pizza. She has $19 to start. Each pizza costs $2. How many pizzas can she get?
  • Quiz 2 - Aiden wants to buy some clothes for his birthday. He has $40. He purchases a white shirt for $14. He spends the rest of the money on black pants. Each pair of pants costs $8. Write an inequality for the number of pairs of pants he can purchase.
  • Quiz 3 - Brooke goes to the market. She purchases a red rose flower for $10 and a lily for $8. She spends the rest of her money on white roses. She has $30 at the start. Each white rose costs $3. How many white roses can she get?

How to Write Word Problems as Inequalities

Do you feel like algebraic word problems are difficult? Don't worry; we'll help to make these word problems as easy as possible. The first and foremost, you need to follow a few steps that will help you solve algebraic word problems. If you stay consistent with this, it will become a habit quickly. Here are some habits you should get in when working with these types of problems:

Step 1) Slow Down and Focus - Read the entire problem thoroughly. Highlight important information and keywords that you think are needed to solve the problem. Those keywords will often present themselves as math operations and comparisons that will help us form and ultimately write our inequality.

Step 2) Determine the Present Conditions - Carefully identify the variables. If there are any values such as coefficients or constants make sure to state those as well. I find it helpful to create an itemized list of all of them and the values associated with them before going any further.

Step 3) Create an Inequality - Take your itemized list and then look for keywords that may indicate relationships between these elements. Some of the phrases you are looking for include:

at least – this indicates a relationship that can be defined as greater than or equal. We use this symbol to signify this: (≥)

less, lesser, less than – indicates a less than (<) relationship.

bigger, larger, or more than – signifies a greater than (>) relationship.

no more than - this indicates a relationship that can be defined as less than or equal. We use this symbol to signify this: (≤)

Once we understand the statement made by the inequality, we place the variable that indicates the condition that needs to be satisfied on one side of the comparison symbol and we arrange the remaining variables and constants on the other side, as stated in the word problem.

Step 4) Solve It For Missing Parts - You can rearrange an inequality much like an equation to solve for a variable. Just consider the compare symbol an equals symbol. Once you have your final answer, realize that inequalities do not give us an exact location of the solution, rather an idea of where the answer lies. Recheck and justify your answer. You can do this by seeing if a fixed value would satisfy the situation that is presented.

Piggy Bank

Example Problem

In a saving account, Sam deposited $400. She wants to have at least $100 in her account by the end of summer. She withdraws $15 every week for food and movie tickets.

Here is how you will write an inequality: First, make sure you highlight the keyword (at least), that will be written down within the inequality as a (≥). Thoroughly read and highlight any other information that you need when writing the inequality. We can identify that she starts with $400 and in the end needs to have $100 or more. We can then identify that every week $15 is being removed from the total. We can rewrite that as 15w, where w is equal to the number of weeks. Here, the variable is the number of weeks since that is what you don't know. Now generating the inequality will be easy; 400 - 15w ≥ 100. We can solve for the number of weeks through these steps:

400 - 15w ≥ 100 (Subtract 400 from both sides)

- 15w ≥ -300 (Divide by -15)

w ≥ 20

This tells us that Sam can live on this budget for 20 weeks.

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