What Is The Solution To − 3 7 M \textless 21 \frac{-3}{7} M \ \textless \ 21 7 − 3 ​ M \textless 21 ?A. M \textless 49 M \ \textless \ 49 M \textless 49 B. M \textgreater 49 M \ \textgreater \ 49 M \textgreater 49 C. M \textgreater − 49 M \ \textgreater \ -49 M \textgreater − 49 D. M \textless − 49 M \ \textless \ -49 M \textless − 49

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Introduction

In mathematics, solving inequalities is a crucial aspect of algebra and is used to determine the range of values that a variable can take. In this article, we will focus on solving the inequality $\frac{-3}{7} m \ \textless \ 21$ and provide a step-by-step guide on how to arrive at the solution.

Understanding the Inequality

The given inequality is $\frac{-3}{7} m \ \textless \ 21$. To solve this inequality, we need to isolate the variable $m$ on one side of the inequality sign. The first step is to multiply both sides of the inequality by $-7$ to get rid of the fraction.

Multiplying Both Sides by $-7$

When we multiply both sides of the inequality by $-7$, we need to remember that this will change the direction of the inequality sign. Since we are multiplying by a negative number, the inequality sign will change from $\textless$ to $\textgreater$.

$\frac{-3}{7} m \ \textless \ 21$

$-7 \times \frac{-3}{7} m \ \textgreater \ -7 \times 21$

This simplifies to:

$3m \ \textgreater \ -147$

Isolating the Variable $m$

Now that we have the inequality $3m \ \textgreater \ -147$, we need to isolate the variable $m$ on one side of the inequality sign. To do this, we can divide both sides of the inequality by $3$.

Dividing Both Sides by $3$

When we divide both sides of the inequality by $3$, we need to remember that this will not change the direction of the inequality sign.

$3m \ \textgreater \ -147$

$\frac{3m}{3} \ \textgreater \ \frac{-147}{3}$

This simplifies to:

$m \ \textgreater \ -49$

Conclusion

In conclusion, the solution to the inequality $\frac{-3}{7} m \ \textless \ 21$ is $m \ \textgreater \ -49$. This means that the value of $m$ must be greater than $-49$ to satisfy the given inequality.

Comparison with the Options

Now that we have the solution to the inequality, let's compare it with the given options.

• Option A: $m \ \textless \ 49$
• Option B: $m \ \textgreater \ 49$
• Option C: $m \ \textgreater \ -49$
• Option D: $m \ \textless \ -49$

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

• Option C: $m \ \textgreater \ -49$

This is because our solution states that $m$ must be greater than $-49$, which is exactly what option C states.

Final Answer

The final answer to the inequality $\frac{-3}{7} m \ \textless \ 21$ is:

$m \ \textgreater \ -49$

This is the correct solution to the given inequality.

Introduction

In our previous article, we discussed how to solve the inequality $\frac{-3}{7} m \ \textless \ 21$. In this article, we will address some of the frequently asked questions (FAQs) related to solving inequalities.

Q: What is an inequality?

A: An inequality is a statement that compares two expressions using a mathematical symbol such as $\textless$, $\textgreater$, $\leq$, or $\geq$. Inequalities are used to describe the relationship between two or more expressions.

Q: What are the different types of inequalities?

A: There are four main types of inequalities:

• Linear inequalities: These are inequalities that involve a linear expression, such as $2x + 3 \ \textless \ 5$.
• Quadratic inequalities: These are inequalities that involve a quadratic expression, such as $x^2 + 4x + 4 \ \textless \ 0$.
• Polynomial inequalities: These are inequalities that involve a polynomial expression, such as $x^3 - 2x^2 + 3x - 1 \ \textless \ 0$.
• Rational inequalities: These are inequalities that involve a rational expression, such as $\frac{x}{x+1} \ \textless \ 2$.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable on one side of the inequality sign. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

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

A: A linear inequality involves a linear expression, whereas a quadratic inequality involves a quadratic expression. For example, $2x + 3 \ \textless \ 5$ is a linear inequality, whereas $x^2 + 4x + 4 \ \textless \ 0$ is a quadratic inequality.

Q: How do I graph an inequality on a number line?

A: To graph an inequality on a number line, you need to plot a point on the number line that satisfies the inequality, and then shade the region to the left or right of the point, depending on the direction of the inequality sign.

Q: What is the solution to an inequality?

A: The solution to an inequality is the set of all values that satisfy the inequality. For example, the solution to the inequality $x \ \textless \ 5$ is the set of all values less than 5, which can be represented as $(-\infty, 5)$.

Q: Can I have multiple solutions to an inequality?

A: Yes, it is possible to have multiple solutions to an inequality. For example, the inequality $x \ \textless \ 5$ has two solutions: $x \ \textless \ 5$ and $x \ \textgreater \ 5$.

Q: How do I check my solution to an inequality?

A: To check your solution to an inequality, you need to plug in a value from the solution set into the original inequality and verify that it is true. If the value satisfies the inequality, then your solution is correct.

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

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

• Not isolating the variable: Make sure to isolate the variable on one side of the inequality sign.
• Not changing the direction of the inequality sign: When multiplying or dividing both sides of the inequality by a negative value, make sure to change the direction of the inequality sign.
• Not checking the solution: Make sure to check your solution to the inequality by plugging in a value from the solution set into the original inequality.

Conclusion

In conclusion, solving inequalities is an important aspect of mathematics that requires careful attention to detail and a thorough understanding of the concepts involved. By following the steps outlined in this article, you can solve inequalities with confidence and accuracy.