At A Supermarket, Every Can Of Tomatoes Weighs At Least 15 Ounces.Let $w$ Represent The Weight Of A Can Of Tomatoes. Which Inequality Represents The Situation?A. $w \leq 15$ B. \$w \ \textless \ 15$[/tex\] C.

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Introduction

Inequalities are mathematical expressions that compare two values or expressions. They are used to represent a wide range of real-world situations, from financial transactions to physical measurements. In this article, we will explore how inequalities can be used to represent a specific situation at a supermarket.

The Situation

At a supermarket, every can of tomatoes weighs at least 15 ounces. This means that the weight of a can of tomatoes is always greater than or equal to 15 ounces. Let's represent the weight of a can of tomatoes as $w$. We want to find an inequality that represents this situation.

Representing the Situation with an Inequality

To represent the situation, we need to use an inequality that states that the weight of a can of tomatoes is greater than or equal to 15 ounces. This can be written as:

w≥15w \geq 15

This inequality states that the weight of a can of tomatoes, $w$, is greater than or equal to 15 ounces.

Comparing the Options

Let's compare the options given in the problem:

A. $w \leq 15$

This option states that the weight of a can of tomatoes is less than or equal to 15 ounces. This is the opposite of what we want to represent.

B. $w \lt 15$

This option states that the weight of a can of tomatoes is less than 15 ounces. This is also the opposite of what we want to represent.

C. $w \geq 15$

This option states that the weight of a can of tomatoes is greater than or equal to 15 ounces. This is the correct representation of the situation.

Conclusion

In conclusion, the correct inequality that represents the situation at the supermarket is:

w≥15w \geq 15

This inequality states that the weight of a can of tomatoes is always greater than or equal to 15 ounces.

Real-World Applications

Inequalities are used in a wide range of real-world situations, from finance to physics. For example, in finance, inequalities can be used to represent the minimum or maximum amount of money that can be invested in a particular stock. In physics, inequalities can be used to represent the minimum or maximum speed of an object.

Solving Inequalities

Solving inequalities involves finding the values of the variable that satisfy the inequality. For example, to solve the inequality $w \geq 15$, we need to find all the values of $w$ that are greater than or equal to 15.

Graphing Inequalities

Graphing inequalities involves representing the inequality on a number line. For example, to graph the inequality $w \geq 15$, we would draw a closed circle at 15 and shade the region to the right of 15.

Common Inequalities

There are several common inequalities that are used in mathematics and real-world applications. Some of these include:

  • Greater than or equal to: $w \geq 15$
  • Less than or equal to: $w \leq 15$
  • Greater than: $w \gt 15$
  • Less than: $w \lt 15$

Tips and Tricks

When working with inequalities, it's essential to remember the following tips and tricks:

  • Read the inequality carefully: Make sure to read the inequality carefully and understand what it's representing.
  • Use the correct symbols: Use the correct symbols to represent the inequality, such as $\geq$ for greater than or equal to.
  • Solve the inequality: Solve the inequality by finding the values of the variable that satisfy the inequality.
  • Graph the inequality: Graph the inequality on a number line to visualize the solution.

Conclusion

Q: What is an inequality?

A: An inequality is a mathematical expression that compares two values or expressions. It is used to represent a wide range of real-world situations, from financial transactions to physical measurements.

Q: What are the different types of inequalities?

A: There are several types of inequalities, including:

  • Greater than or equal to: $w \geq 15$
  • Less than or equal to: $w \leq 15$
  • Greater than: $w \gt 15$
  • Less than: $w \lt 15$

Q: How do I solve an inequality?

A: To solve an inequality, you need to find the values of the variable that satisfy the inequality. This can be done by:

  • Isolating the variable: Isolate the variable on one side of the inequality.
  • Simplifying the inequality: Simplify the inequality by combining like terms.
  • Graphing the inequality: Graph the inequality on a number line to visualize the solution.

Q: What is the difference between an inequality and an equation?

A: An equation is a mathematical expression that states that two values or expressions are equal. An inequality, on the other hand, states that two values or expressions are not equal.

Q: How do I graph an inequality?

A: To graph an inequality, you need to:

  • Draw a number line: Draw a number line and mark the point that represents the value of the variable.
  • Draw a closed circle: Draw a closed circle at the point that represents the value of the variable if the inequality is greater than or equal to.
  • Draw an open circle: Draw an open circle at the point that represents the value of the variable if the inequality is less than or equal to.
  • Shade the region: Shade the region to the right of the point if the inequality is greater than or equal to, or to the left of the point if the inequality is less than or equal to.

Q: What are some common applications of inequalities?

A: Inequalities have many applications in real-world situations, including:

  • Finance: Inequalities can be used to represent the minimum or maximum amount of money that can be invested in a particular stock.
  • Physics: Inequalities can be used to represent the minimum or maximum speed of an object.
  • Engineering: Inequalities can be used to represent the minimum or maximum stress on a material.

Q: How do I determine the correct inequality to use in a given situation?

A: To determine the correct inequality to use in a given situation, you need to:

  • Read the problem carefully: Read the problem carefully and understand what is being asked.
  • Identify the variable: Identify the variable that is being compared.
  • Determine the relationship: Determine the relationship between the variable and the value or expression being compared.

Q: What are some common mistakes to avoid when working with inequalities?

A: Some common mistakes to avoid when working with inequalities include:

  • Not reading the inequality carefully: Not reading the inequality carefully can lead to incorrect solutions.
  • Using the wrong symbols: Using the wrong symbols can lead to incorrect solutions.
  • Not solving the inequality correctly: Not solving the inequality correctly can lead to incorrect solutions.

Conclusion

In conclusion, inequalities are a fundamental concept in mathematics and have many applications in real-world situations. By understanding how to represent and solve inequalities, you can better analyze and solve problems in a wide range of fields.