Solve For $x$:$\sqrt{(5x + 5)} + 40 = 50$A. 19B. 319C. 499D. 1.619

Introduction

Radical equations are a type of algebraic equation that involves a variable under a radical sign. In this article, we will focus on solving a specific radical equation of the form $\sqrt{(5x + 5)} + 40 = 50$. This equation involves a square root and a linear term, and we will use algebraic techniques to isolate the variable $x$.

Understanding the Equation

The given equation is $\sqrt{(5x + 5)} + 40 = 50$. Our goal is to solve for $x$, which means we need to isolate the variable $x$ on one side of the equation. To do this, we will use algebraic techniques such as subtracting, adding, multiplying, and dividing.

Step 1: Subtract 40 from Both Sides

The first step in solving the equation is to subtract 40 from both sides of the equation. This will help us isolate the square root term.

$\sqrt{(5x + 5)} + 40 - 40 = 50 - 40$

Simplifying the equation, we get:

$\sqrt{(5x + 5)} = 10$

Step 2: Square Both Sides

The next step is to square both sides of the equation. This will help us eliminate the square root sign.

$(\sqrt{(5x + 5)})^2 = 10^2$

Simplifying the equation, we get:

$5x + 5 = 100$

Step 3: Subtract 5 from Both Sides

The next step is to subtract 5 from both sides of the equation. This will help us isolate the term involving $x$.

$5x + 5 - 5 = 100 - 5$

Simplifying the equation, we get:

$5x = 95$

Step 4: Divide Both Sides by 5

The final step is to divide both sides of the equation by 5. This will help us solve for $x$.

$\frac{5x}{5} = \frac{95}{5}$

Simplifying the equation, we get:

$x = 19$

Conclusion

In this article, we solved a radical equation of the form $\sqrt{(5x + 5)} + 40 = 50$. We used algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation. The final solution is $x = 19$.

Answer

The correct answer is A. 19.

Tips and Tricks

• When solving radical equations, it's essential to isolate the square root term first.
• Use algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$.
• Be careful when squaring both sides of the equation, as this can introduce extraneous solutions.

Practice Problems

• Solve the equation $\sqrt{(3x - 2)} + 20 = 30$.
• Solve the equation $\sqrt{(2x + 1)} - 10 = 5$.

References

• [1] "Algebra and Trigonometry" by Michael Sullivan
• [2] "College Algebra" by James Stewart

Category

• Mathematics
• Algebra
• Radical Equations
  Solving for x in a Radical Equation: Q&A =====================================================

Introduction

In our previous article, we solved a radical equation of the form $\sqrt{(5x + 5)} + 40 = 50$. We used algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation. In this article, we will answer some frequently asked questions about solving radical equations.

Q: What is a radical equation?

A: A radical equation is a type of algebraic equation that involves a variable under a radical sign. It is an equation that contains a square root or other radical expression.

Q: How do I solve a radical equation?

A: To solve a radical equation, you need to isolate the square root term first. Then, you can use algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation.

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

A: Some common mistakes to avoid when solving radical equations include:

• Not isolating the square root term first
• Squaring both sides of the equation without checking for extraneous solutions
• Not checking for extraneous solutions after squaring both sides of the equation

Q: How do I check for extraneous solutions?

A: To check for extraneous solutions, you need to plug the solution back into the original equation and check if it is true. If the solution is not true, then it is an extraneous solution.

Q: What is an extraneous solution?

A: An extraneous solution is a solution that is not a valid solution to the equation. It is a solution that is introduced when you square both sides of the equation.

Q: How do I know if a solution is an extraneous solution?

A: To determine if a solution is an extraneous solution, you need to plug the solution back into the original equation and check if it is true. If the solution is not true, then it is an extraneous solution.

Q: Can I use a calculator to solve radical equations?

A: Yes, you can use a calculator to solve radical equations. However, you need to be careful when using a calculator to solve radical equations, as it may introduce errors.

Q: What are some tips for solving radical equations?

A: Some tips for solving radical equations include:

• Isolate the square root term first
• Use algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation
• Check for extraneous solutions after squaring both sides of the equation
• Use a calculator to check your solutions

Conclusion

In this article, we answered some frequently asked questions about solving radical equations. We discussed common mistakes to avoid, how to check for extraneous solutions, and some tips for solving radical equations.

Answer

The correct answers to the questions are:

• Q: What is a radical equation? A: A radical equation is a type of algebraic equation that involves a variable under a radical sign.
• Q: How do I solve a radical equation? A: To solve a radical equation, you need to isolate the square root term first. Then, you can use algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation.
• Q: What are some common mistakes to avoid when solving radical equations? A: Some common mistakes to avoid when solving radical equations include not isolating the square root term first, squaring both sides of the equation without checking for extraneous solutions, and not checking for extraneous solutions after squaring both sides of the equation.
• Q: How do I check for extraneous solutions? A: To check for extraneous solutions, you need to plug the solution back into the original equation and check if it is true. If the solution is not true, then it is an extraneous solution.
• Q: What is an extraneous solution? A: An extraneous solution is a solution that is not a valid solution to the equation. It is a solution that is introduced when you square both sides of the equation.
• Q: How do I know if a solution is an extraneous solution? A: To determine if a solution is an extraneous solution, you need to plug the solution back into the original equation and check if it is true. If the solution is not true, then it is an extraneous solution.
• Q: Can I use a calculator to solve radical equations? A: Yes, you can use a calculator to solve radical equations. However, you need to be careful when using a calculator to solve radical equations, as it may introduce errors.
• Q: What are some tips for solving radical equations? A: Some tips for solving radical equations include isolating the square root term first, using algebraic techniques such as subtracting, adding, multiplying, and dividing to isolate the variable $x$ on one side of the equation, checking for extraneous solutions after squaring both sides of the equation, and using a calculator to check your solutions.

Category

• Mathematics
• Algebra
• Radical Equations