Solve For C C C : − 2 C + 13.2 \textless 9.2 -2c + 13.2 \ \textless \ 9.2 − 2 C + 13.2 \textless 9.2 Choose The Correct Inequality:A. $c \ \textgreater \ $B. $c \ \textless \ $C. C ≥ C \geq C ≥ D. C ≤ C \leq C ≤

Mar 13, 2025 by ADMIN 216 views

Solving Linear Inequalities: A Step-by-Step Guide

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Introduction

Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a specific linear inequality, $-2c + 13.2 < 9.2$ , and provide a step-by-step guide on how to choose the correct inequality.

Understanding Linear Inequalities

A linear inequality is an inequality that involves a linear expression, which is an expression that can be written in the form $ax + b$ , where $a$ and $b$ are constants and $x$ is the variable. Linear inequalities can be written in the following forms:

$ax + b < c$
$ax + b > c$
$ax + b \leq c$
$ax + b \geq c$

Solving the Inequality

To solve the inequality $-2c + 13.2 < 9.2$ , we need to isolate the variable $c$ . We can do this by subtracting $13.2$ from both sides of the inequality and then dividing both sides by $-2$ .

Step 1: Subtract 13.2 from both sides

$-2c + 13.2 - 13.2 < 9.2 - 13.2$

This simplifies to:

$-2c < -4$

Step 2: Divide both sides by -2

To divide both sides by $-2$ , we need to remember that when we divide or multiply an inequality by a negative number, we need to reverse the direction of the inequality.

$\frac{-2c}{-2} > \frac{-4}{-2}$

This simplifies to:

$c > 2$

Choosing the Correct Inequality

Now that we have solved the inequality, we need to choose the correct inequality from the options provided.

A. $c > 2$
B. $c < 2$
C. $c \geq 2$
D. $c \leq 2$

Based on our solution, we can see that the correct inequality is:

A. $c > 2$

Conclusion

Solving linear inequalities requires a step-by-step approach, and it is essential to understand the properties of linear expressions and inequalities. By following the steps outlined in this article, you can solve linear inequalities with confidence. Remember to always check your solution by plugging in values to ensure that it is correct.

Frequently Asked Questions

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that involves a linear expression, while a linear inequality is an inequality that involves a linear expression.

Q: How do I solve a linear inequality with a negative coefficient?

A: To solve a linear inequality with a negative coefficient, you need to reverse the direction of the inequality when you divide or multiply both sides by a negative number.

Q: What is the importance of solving linear inequalities?

A: Solving linear inequalities is essential in mathematics, as it helps to model real-world problems and make predictions about the behavior of variables.

Final Thoughts

Solving linear inequalities is a crucial skill for students to master, and it requires a step-by-step approach. By following the steps outlined in this article, you can solve linear inequalities with confidence. Remember to always check your solution by plugging in values to ensure that it is correct.

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Introduction

Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a comprehensive Q&A section on linear inequalities, covering various topics and concepts.

Q&A Section

Q: What is a linear inequality?

A: A linear inequality is an inequality that involves a linear expression, which is an expression that can be written in the form $ax + b$ , where $a$ and $b$ are constants and $x$ is the variable.

Q: What are the different types of linear inequalities?

A: There are four types of linear inequalities:

$ax + b < c$
$ax + b > c$
$ax + b \leq c$
$ax + b \geq c$

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable by performing the same operations on both sides of the inequality. You can add or subtract the same value from both sides, or multiply or divide both sides by the same non-zero value.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that involves a linear expression, while a linear inequality is an inequality that involves a linear expression.

Q: How do I solve a linear inequality with a negative coefficient?

A: To solve a linear inequality with a negative coefficient, you need to reverse the direction of the inequality when you divide or multiply both sides by a negative number.

Q: What is the importance of solving linear inequalities?

A: Solving linear inequalities is essential in mathematics, as it helps to model real-world problems and make predictions about the behavior of variables.

Q: Can I use the same methods to solve linear inequalities as I do to solve linear equations?

A: Yes, you can use the same methods to solve linear inequalities as you do to solve linear equations, such as adding or subtracting the same value from both sides, or multiplying or dividing both sides by the same non-zero value.

Q: How do I check my solution to a linear inequality?

A: To check your solution to a linear inequality, you can plug in values to ensure that the inequality is true. For example, if you have the inequality $x > 2$ , you can plug in values such as $x = 3$ or $x = 4$ to see if the inequality is true.

Q: Can I use a calculator to solve linear inequalities?

A: Yes, you can use a calculator to solve linear inequalities, but you need to be careful when using a calculator to solve inequalities. Make sure to check your solution by plugging in values to ensure that the inequality is true.

Q: What are some common mistakes to avoid when solving linear inequalities?

A: Some common mistakes to avoid when solving linear inequalities include:

Not reversing the direction of the inequality when dividing or multiplying both sides by a negative number
Not checking the solution by plugging in values
Not using the same operations on both sides of the inequality

Conclusion

Solving linear inequalities requires a step-by-step approach, and it is essential to understand the properties of linear expressions and inequalities. By following the steps outlined in this article and avoiding common mistakes, you can solve linear inequalities with confidence.

Frequently Asked Questions (FAQs)

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that involves a linear expression, while a quadratic inequality is an inequality that involves a quadratic expression.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you need to factor the quadratic expression and then use the sign chart method to determine the solution.

Q: What is the sign chart method?

A: The sign chart method is a technique used to solve quadratic inequalities by creating a chart to determine the sign of the quadratic expression in different intervals.

Final Thoughts

Solving linear inequalities is a crucial skill for students to master, and it requires a step-by-step approach. By following the steps outlined in this article and avoiding common mistakes, you can solve linear inequalities with confidence. Remember to always check your solution by plugging in values to ensure that the inequality is true.