What Are The Two Equations Created By The Inequality ∣ X − 12 ∣ + 5 \textless 27 |x-12|+5\ \textless \ 27 ∣ X − 12∣ + 5 \textless 27 ? Y 1 = Y_1 = Y 1 ​ = $\square$ And Y 2 = Y_2 = Y 2 ​ = $\square$

Introduction

In mathematics, inequalities are used to describe the relationship between two or more expressions. They can be used to find the range of values for a variable, and they can also be used to solve equations. In this article, we will explore the inequality $|x-12|+5\ \textless \ 27$ and find the two equations that are created by it.

Understanding the Inequality

The given inequality is $|x-12|+5\ \textless \ 27$. To solve this inequality, we need to isolate the absolute value expression. We can do this by subtracting 5 from both sides of the inequality, which gives us $|x-12|\ \textless \ 22$.

Solving the Inequality

To solve the inequality $|x-12|\ \textless \ 22$, we need to consider two cases: when $x-12$ is positive and when $x-12$ is negative.

Case 1: $x-12$ is Positive

When $x-12$ is positive, the absolute value expression $|x-12|$ is equal to $x-12$. So, the inequality becomes $x-12\ \textless \ 22$. We can add 12 to both sides of the inequality to get $x\ \textless \ 34$.

Case 2: $x-12$ is Negative

When $x-12$ is negative, the absolute value expression $|x-12|$ is equal to $-(x-12)$. So, the inequality becomes $-(x-12)\ \textless \ 22$. We can simplify this inequality by multiplying both sides by -1, which gives us $x-12\ \textgreater \ -22$. We can add 12 to both sides of the inequality to get $x\ \textgreater \ -10$.

Finding the Two Equations

Now that we have solved the inequality, we can find the two equations that are created by it. The two equations are the boundary lines of the inequality. The first equation is $x=34$, which is the boundary line for the case when $x-12$ is positive. The second equation is $x=-10$, which is the boundary line for the case when $x-12$ is negative.

Conclusion

In this article, we have explored the inequality $|x-12|+5\ \textless \ 27$ and found the two equations that are created by it. The two equations are $x=34$ and $x=-10$. These equations represent the boundary lines of the inequality, and they can be used to find the range of values for the variable x.

Final Answer

The two equations created by the inequality $|x-12|+5\ \textless \ 27$ are:

• $y_1 =$ 34
• $y_2 =$ -10

Note: The final answer is in the format of $y_1 =$ and $y_2 =$, where $y_1$ and $y_2$ are the two equations created by the inequality.

Introduction

In our previous article, we explored the inequality $|x-12|+5\ \textless \ 27$ and found the two equations that are created by it. In this article, we will answer some frequently asked questions (FAQs) about the inequality and its solutions.

Q&A

Q: What is the meaning of the absolute value expression $|x-12|$?

A: The absolute value expression $|x-12|$ represents the distance between x and 12 on the number line. It is always non-negative, and it is equal to x-12 when x-12 is positive, and -(x-12) when x-12 is negative.

Q: How do I solve the inequality $|x-12|+5\ \textless \ 27$?

A: To solve the inequality, you need to isolate the absolute value expression. You can do this by subtracting 5 from both sides of the inequality, which gives you $|x-12|\ \textless \ 22$. Then, you need to consider two cases: when $x-12$ is positive and when $x-12$ is negative.

Q: What are the two equations created by the inequality $|x-12|+5\ \textless \ 27$?

A: The two equations created by the inequality are $x=34$ and $x=-10$. These equations represent the boundary lines of the inequality, and they can be used to find the range of values for the variable x.

Q: How do I graph the inequality $|x-12|+5\ \textless \ 27$?

A: To graph the inequality, you need to graph the two boundary lines $x=34$ and $x=-10$. Then, you need to shade the region between the two lines, which represents the solution to the inequality.

Q: Can I use the inequality $|x-12|+5\ \textless \ 27$ to solve other problems?

A: Yes, you can use the inequality $|x-12|+5\ \textless \ 27$ to solve other problems. For example, you can use it to find the range of values for a variable that satisfies a certain condition.

Q: How do I check my solution to the inequality $|x-12|+5\ \textless \ 27$?

A: To check your solution, you need to plug in a value of x that satisfies the inequality and see if it is true. If it is true, then your solution is correct.

Conclusion

In this article, we have answered some frequently asked questions (FAQs) about the inequality $|x-12|+5\ \textless \ 27$ and its solutions. We hope that this article has been helpful in clarifying any doubts you may have had about the inequality and its solutions.

Final Answer

The two equations created by the inequality $|x-12|+5\ \textless \ 27$ are:

• $y_1 =$ 34
• $y_2 =$ -10

Note: The final answer is in the format of $y_1 =$ and $y_2 =$, where $y_1$ and $y_2$ are the two equations created by the inequality.