Not subtracting 4 from both sides of the inequality

Oct 13, 2025 by talynt.org 115 views

Introduction

In algebra, isolating a variable is a crucial step in solving equations and inequalities. It involves manipulating the equation to get the variable by itself on one side of the equation. In this article, we will learn how to isolate the variable to solve the inequality $4x + 4 \ \textgreater \ -20$ . We will also determine which number line shows the solution set.

Understanding the Inequality

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

Subtracting 4 from Both Sides

When we subtract 4 from both sides of the inequality, we get:

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

This simplifies to:

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 get rid of the coefficient of $x$ , which is 4. We can do this by dividing both sides of the inequality by 4.

Dividing Both Sides by 4

When we divide both sides of the inequality by 4, we get:

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

This simplifies to:

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.

Number Line Representation

To represent the solution set on a number line, we draw a line and mark a point at -6. We then shade the region to the right of the point, indicating that all values greater than -6 are part of the solution set.

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 the solution set on a number line by drawing a line at -6 and shading the region to the right of the point.

Frequently Asked Questions

What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$ ? The solution set is all values of $x$ that are greater than -6.
How do I represent the solution set on a number line? To represent the solution set on a number line, draw a line at -6 and shade the region to the right of the point.
What is the first step in solving the inequality $4x + 4 \ \textgreater \ -20$ ? The first step is to subtract 4 from both sides of the inequality.

Step-by-Step Solution

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: $x \ \textgreater \ -6$

Common Mistakes to Avoid

Not subtracting 4 from both sides of the inequality: This will result in an incorrect solution set.
Not dividing both sides of the inequality by 4: This will also result in an incorrect solution set.
Not simplifying the inequality: This will make it difficult to determine the solution set.

Real-World Applications

Finance: In finance, inequalities are used to model real-world problems, such as determining the minimum amount of money needed to invest in a stock.
Science: In science, inequalities are used to model real-world problems, such as determining the maximum temperature of a chemical reaction.
Engineering: In engineering, inequalities are used to model real-world problems, such as determining the minimum amount of material needed to build a structure.

Conclusion

In conclusion, isolating a variable is a crucial step in solving equations and inequalities. In this article, we learned how to isolate the variable to solve the inequality $4x + 4 \ \textgreater \ -20$ . We also determined which number line shows the solution set. By following the steps outlined in this article, you can solve inequalities and represent the solution set on a number line.

Introduction

In our previous article, we learned how to isolate the variable to solve the inequality $4x + 4 \ \textgreater \ -20$ . We also determined which number line shows the solution set. In this article, we will answer some frequently asked questions about isolating the variable to solve inequalities.

Q&A

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

A: The first step is to subtract 4 from both sides 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 on the left-hand side.

Q: What is the next step after subtracting 4 from both sides of the inequality?

A: The next step is to divide both sides of the inequality by 4.

Q: Why do we need to divide both sides of the inequality by 4?

A: We need to divide both sides of the inequality by 4 to get rid of the coefficient of $x$ .

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: To represent the solution set on a number line, draw a line at -6 and shade the region to the right of the point.

Q: What is the difference between an equation and an inequality?

A: An equation is a statement that says two expressions are equal, while an inequality is a statement that says one expression is greater than or less than another expression.

Q: Can I use the same steps to solve an equation as I would to solve an inequality?

A: No, the steps to solve an equation and an inequality are different.

Q: What is the importance of isolating the variable in solving inequalities?

A: Isolating the variable is important because it allows us to determine the solution set of the inequality.

Q: Can I use a calculator to solve inequalities?

A: Yes, you can use a calculator to solve inequalities, but it's not always necessary.

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

A: Some common mistakes to avoid when solving inequalities include not subtracting the constant term from both sides, not dividing both sides by the coefficient of $x$ , and not simplifying the inequality.

Conclusion

In conclusion, isolating the variable is a crucial step in solving inequalities. By following the steps outlined in this article, you can solve inequalities and represent the solution set on a number line. Remember to avoid common mistakes and use a calculator if necessary.

Frequently Asked Questions

What is the solution set of the inequality $4x + 4 \ \textgreater \ -20$ ? The solution set is all values of $x$ that are greater than -6.
How do I represent the solution set on a number line? To represent the solution set on a number line, draw a line at -6 and shade the region to the right of the point.
What is the first step in solving the inequality $4x + 4 \ \textgreater \ -20$ ? The first step is to subtract 4 from both sides of the inequality.

Step-by-Step Solution

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: $x \ \textgreater \ -6$

Common Mistakes to Avoid

Not subtracting 4 from both sides of the inequality: This will result in an incorrect solution set.
Not dividing both sides of the inequality by 4: This will also result in an incorrect solution set.
Not simplifying the inequality: This will make it difficult to determine the solution set.

Real-World Applications

Finance: In finance, inequalities are used to model real-world problems, such as determining the minimum amount of money needed to invest in a stock.
Science: In science, inequalities are used to model real-world problems, such as determining the maximum temperature of a chemical reaction.
Engineering: In engineering, inequalities are used to model real-world problems, such as determining the minimum amount of material needed to build a structure.