Isolate The Variable To Solve $4x + 4 \ \textgreater \ -20$. Which Number Line Shows The Solution Set?

Feb 26, 2025 by ADMIN 107 views

$Isolate the Variable to Solve the Inequality $4x + 4 \ \textgreater \ -20$$

Introduction

In mathematics, solving inequalities is a crucial concept that helps us understand the relationship between variables and their values. When we are given an inequality, our goal is to isolate the variable, which means we need to get the variable by itself on one side of the inequality sign. In this article, we will focus on solving the inequality $4x + 4 \ \textgreater \ -20$ and determine which number line shows the solution set.

Understanding the Inequality

The given inequality is $4x + 4 \ \textgreater \ -20$. To solve this inequality, we need to isolate the variable x. The first step is to subtract 4 from both sides of the inequality. This will help us get rid of the constant term on the left-hand side.

4x + 4 - 4 \ \textgreater \ -20 - 4

4x \ \textgreater \ -24

Isolating the Variable

Now that we have the inequality $4x \ \textgreater \ -24$, we need to isolate the variable x. To do this, we need to divide both sides of the inequality by 4. This will help us get rid of the coefficient of x.

\frac{4x}{4} \ \textgreater \ \frac{-24}{4}

x \ \textgreater \ -6

Understanding the Solution Set

The solution set of an inequality is the set of all values of the variable that satisfy the inequality. In this case, the solution set is all values of x that are greater than -6. This means that any value of x that is greater than -6 will make the inequality true.

Number Line Representation

To represent the solution set on a number line, we need to draw a line that shows all values of x that are greater than -6. We can do this by drawing a line that starts at -6 and extends to the right.

Conclusion

In conclusion, to solve the inequality $4x + 4 \ \textgreater \ -20$, we need to isolate the variable x. We can do this by subtracting 4 from both sides of the inequality and then dividing both sides by 4. The solution set is all values of x that are greater than -6. We can represent this solution set on a number line by drawing a line that starts at -6 and extends to the right.

Step-by-Step Solution

Here is a step-by-step solution to the inequality:

Subtract 4 from both sides of the inequality: $4x + 4 - 4 \ \textgreater \ -20 - 4$
Simplify the inequality: $4x \ \textgreater \ -24$
Divide both sides of the inequality by 4: $\frac{4x}{4} \ \textgreater \ \frac{-24}{4}$
Simplify the inequality: $x \ \textgreater \ -6$

Frequently Asked Questions

What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$?
How do we represent the solution set on a number line?
What is the value of x that satisfies the inequality?

Answer

The solution set of the inequality $4x + 4 \ \textgreater \ -20$ is all values of x that are greater than -6.
We can represent the solution set on a number line by drawing a line that starts at -6 and extends to the right.
The value of x that satisfies the inequality is any value greater than -6.

Final Answer

The final answer is: $\boxed{-6}$

Introduction

In our previous article, we discussed how to isolate the variable to solve the inequality $4x + 4 \ \textgreater \ -20$. We learned how to subtract 4 from both sides of the inequality and then divide both sides by 4 to get the solution set. In this article, we will answer some frequently asked questions related to the inequality and provide additional information to help you understand the concept better.

Q&A

Q: What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$?

A: The solution set of the inequality $4x + 4 \ \textgreater \ -20$ is all values of x that are greater than -6.

Q: How do we represent the solution set on a number line?

A: We can represent the solution set on a number line by drawing a line that starts at -6 and extends to the right.

Q: What is the value of x that satisfies the inequality?

A: The value of x that satisfies the inequality is any value greater than -6.

Q: Can we use the same steps to solve the inequality $4x + 4 \ \textless \ -20$?

A: No, we cannot use the same steps to solve the inequality $4x + 4 \ \textless \ -20$. The inequality sign is different, and we need to use a different approach to solve it.

Q: How do we know which direction to extend the number line?

A: We know which direction to extend the number line by looking at the inequality sign. If the inequality sign is greater than (>, we extend the number line to the right. If the inequality sign is less than (<, we extend the number line to the left.

Q: Can we use the same steps to solve the inequality $4x - 4 \ \textgreater \ -20$?

A: Yes, we can use the same steps to solve the inequality $4x - 4 \ \textgreater \ -20$. We can add 4 to both sides of the inequality and then divide both sides by 4 to get the solution set.

Q: How do we know if the inequality is true or false?

A: We can determine if the inequality is true or false by plugging in a value of x that satisfies the inequality. If the inequality is true, then the value of x will make the inequality true.

Additional Tips

When solving inequalities, make sure to use the correct inequality sign.
When representing the solution set on a number line, make sure to extend the line in the correct direction.
When plugging in a value of x to test the inequality, make sure to use a value that satisfies the inequality.