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

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Introduction

In algebra, solving inequalities involves isolating the variable to determine its solution set. The given inequality $4x + 4 \ \textgreater \ -20$ requires us to isolate the variable $x$ to find the values that satisfy the inequality. In this article, we will guide you through the steps to isolate the variable and determine the solution set.

Understanding the Inequality

The given inequality is $4x + 4 \ \textgreater \ -20$. To isolate the variable $x$, we need to get rid of the constant term $4$ on the left-hand side of the inequality. We can do this by subtracting $4$ from both sides of the inequality.

Subtracting 4 from Both Sides

Subtracting $4$ from both sides of the inequality gives us:

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

Simplifying the left-hand side, we get:

$$4x \ \textgreater \ -24$$

Dividing by 4

To isolate the variable $x$, we need to get rid of the coefficient $4$ on the left-hand side of the inequality. We can do this by dividing both sides of the inequality by $4$.

However, when we divide both sides of an inequality by a negative number, the direction of the inequality sign changes. In this case, we are dividing by $4$, which is positive. Therefore, the direction of the inequality sign remains the same.

Dividing both sides of the inequality by $4$ gives us:

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

Simplifying the left-hand side, we get:

$$x \ \textgreater \ -6$$

Understanding the Solution Set

The solution set of an inequality is the set of all values that satisfy the inequality. In this case, the solution set is all values of $x$ that are greater than $-6$. This can be represented on a number line as follows:

Number Line Representation

The number line representation of the solution set is a line that extends to the right of $-6$. This indicates that all values of $x$ greater than $-6$ satisfy the inequality.

Conclusion

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

Step-by-Step Solution

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

1. Subtract $4$ from both sides of the inequality: $4x + 4 - 4 \ \textgreater \ -20 - 4$
2. Simplify the left-hand side: $4x \ \textgreater \ -24$
3. Divide both sides of the inequality by $4$: $\frac{4x}{4} \ \textgreater \ \frac{-24}{4}$
4. Simplify the left-hand side: $x \ \textgreater \ -6$

Frequently Asked Questions

• Q: What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$? A: The solution set is all values of $x$ that are greater than $-6$.
• Q: How do I represent the solution set on a number line? A: The solution set can be represented on a number line as a line that extends to the right of $-6$.
• Q: What is the first step to solve the inequality $4x + 4 \ \textgreater \ -20$? A: The first step is to subtract $4$ from both sides of the inequality.

Final Answer

The final answer is $\boxed{x \ \textgreater \ -6}$.

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Introduction

In our previous article, we solved the inequality $4x + 4 \ \textgreater \ -20$ by isolating the variable $x$. In this article, we will provide a Q&A section to help you better understand the solution and address any questions you may have.

Q&A

Q: What is the first step to solve the inequality $4x + 4 \ \textgreater \ -20$?

A: The first step is to subtract $4$ from both sides of the inequality. This will help us get rid of the constant term $4$ on the left-hand side of the inequality.

Q: Why do we need to subtract $4$ from both sides of the inequality?

A: We need to subtract $4$ from both sides of the inequality to get rid of the constant term $4$ on the left-hand side of the inequality. This will help us isolate the variable $x$.

Q: What happens when we divide both sides of the inequality by $4$?

A: When we divide both sides of the inequality by $4$, the direction of the inequality sign remains the same. This is because $4$ is a positive number.

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

A: The solution set is all values of $x$ that are greater than $-6$. This can be represented on a number line as a line that extends to the right of $-6$.

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

A: The solution set can be represented on a number line as a line that extends to the right of $-6$. This indicates that all values of $x$ greater than $-6$ satisfy the inequality.

Q: What is the final answer to the inequality $4x + 4 \ \textgreater \ -20$?

A: The final answer is $\boxed{x \ \textgreater \ -6}$.

Q: Can I use a calculator to solve the inequality $4x + 4 \ \textgreater \ -20$?

A: While a calculator can be used to solve the inequality, it is not necessary. The solution can be found by following the steps outlined in our previous article.

Q: What if I get stuck while solving the inequality $4x + 4 \ \textgreater \ -20$?

A: If you get stuck while solving the inequality, you can try breaking it down into smaller steps or seeking help from a teacher or tutor.

Conclusion

In conclusion, solving the inequality $4x + 4 \ \textgreater \ -20$ requires us to isolate the variable $x$ by subtracting $4$ from both sides and then dividing by $4$. The solution set is all values of $x$ that are greater than $-6$, which can be represented on a number line as a line that extends to the right of $-6$. We hope this Q&A section has helped you better understand the solution and address any questions you may have.

Step-by-Step Solution

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

1. Subtract $4$ from both sides of the inequality: $4x + 4 - 4 \ \textgreater \ -20 - 4$
2. Simplify the left-hand side: $4x \ \textgreater \ -24$
3. Divide both sides of the inequality by $4$: $\frac{4x}{4} \ \textgreater \ \frac{-24}{4}$
4. Simplify the left-hand side: $x \ \textgreater \ -6$

Frequently Asked Questions

• Q: What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$? A: The solution set is all values of $x$ that are greater than $-6$.
• Q: How do I represent the solution set on a number line? A: The solution set can be represented on a number line as a line that extends to the right of $-6$.
• Q: What is the first step to solve the inequality $4x + 4 \ \textgreater \ -20$? A: The first step is to subtract $4$ from both sides of the inequality.

Final Answer

The final answer is $\boxed{x \ \textgreater \ -6}$.