What Value Of $x$ Is In The Solution Set Of The Inequality $9(2x + 1) \ \textless \ 9x - 18$?A. − 4 -4 − 4 B. − 3 -3 − 3 C. − 2 -2 − 2 D. − 1 -1 − 1
Introduction
In mathematics, inequalities are a fundamental concept that help us compare the values of different expressions. Solving inequalities involves finding the values of the variable that satisfy the given inequality. In this article, we will focus on solving the inequality $9(2x + 1) \ \textless \ 9x - 18$ and finding the value of $x$ that is in the solution set.
Understanding the Inequality
The given inequality is $9(2x + 1) \ \textless \ 9x - 18$. To solve this inequality, we need to isolate the variable $x$. The first step is to expand the left-hand side of the inequality using the distributive property.
Now, the inequality becomes:
Isolating the Variable
To isolate the variable $x$, we need to get all the terms involving $x$ on one side of the inequality. We can do this by subtracting $9x$ from both sides of the inequality.
Simplifying the inequality, we get:
Solving for $x$
Now, we need to isolate the variable $x$ by subtracting $9$ from both sides of the inequality.
Simplifying the inequality, we get:
Final Step
To solve for $x$, we need to divide both sides of the inequality by $9$.
Simplifying the inequality, we get:
Conclusion
In conclusion, the value of $x$ that is in the solution set of the inequality $9(2x + 1) \ \textless \ 9x - 18$ is $x \ \textless \ -3$. This means that any value of $x$ that is less than $-3$ will satisfy the given inequality.
Final Answer
The final answer is:
Introduction
In our previous article, we solved the inequality $9(2x + 1) \ \textless \ 9x - 18$ and found that the value of $x$ that is in the solution set is $x \ \textless \ -3$. In this article, we will answer some frequently asked questions related to solving this inequality.
Q: What is the first step in solving the inequality $9(2x + 1) \ \textless \ 9x - 18$?
A: The first step in solving the inequality is to expand the left-hand side of the inequality using the distributive property. This gives us $18x + 9 \ \textless \ 9x - 18$.
Q: How do we isolate the variable $x$ in the inequality $18x + 9 \ \textless \ 9x - 18$?
A: To isolate the variable $x$, we need to get all the terms involving $x$ on one side of the inequality. We can do this by subtracting $9x$ from both sides of the inequality.
Q: What is the next step in solving the inequality after isolating the variable $x$?
A: After isolating the variable $x$, we need to simplify the inequality by combining like terms. This gives us $9x + 9 \ \textless \ -18$.
Q: How do we solve for $x$ in the inequality $9x + 9 \ \textless \ -18$?
A: To solve for $x$, we need to subtract $9$ from both sides of the inequality. This gives us $9x \ \textless \ -27$.
Q: What is the final step in solving the inequality $9x \ \textless \ -27$?
A: The final step in solving the inequality is to divide both sides of the inequality by $9$. This gives us $x \ \textless \ -3$.
Q: What is the solution set of the inequality $9(2x + 1) \ \textless \ 9x - 18$?
A: The solution set of the inequality is all values of $x$ that are less than $-3$.
Q: Can we write the solution set of the inequality in interval notation?
A: Yes, we can write the solution set of the inequality in interval notation as $(-\infty, -3)$.
Q: How do we graph the solution set of the inequality on a number line?
A: To graph the solution set of the inequality on a number line, we draw a closed circle at $-3$ and shade all the numbers to the left of $-3$.
Q: What is the final answer to the inequality $9(2x + 1) \ \textless \ 9x - 18$?
A: The final answer to the inequality is $x \ \textless \ -3$.
Conclusion
In conclusion, solving the inequality $9(2x + 1) \ \textless \ 9x - 18$ involves expanding the left-hand side of the inequality, isolating the variable $x$, simplifying the inequality, and solving for $x$. The solution set of the inequality is all values of $x$ that are less than $-3$.
Final Answer
The final answer is: