What Is The Solution To The Equation Below?$\sqrt{5x-2}-1=3$A. $x=\frac{4}{5}$ B. $x=\frac{18}{5}$ C. $x=\frac{14}{5}$ D. $x=\frac{6}{5}$

Introduction

Mathematics is a subject that deals with numbers, quantities, and shapes. It is a fundamental subject that is used in various fields such as science, engineering, economics, and finance. In mathematics, equations are used to represent relationships between variables. Solving equations is an essential skill in mathematics, and it is used to find the value of unknown variables.

Understanding the Equation

The given equation is $\sqrt{5x-2}-1=3$. This equation involves a square root and a variable $x$. The objective is to solve for the value of $x$.

Breaking Down the Equation

To solve the equation, we need to isolate the variable $x$. The first step is to add $1$ to both sides of the equation to get rid of the negative term.

$\sqrt{5x-2}-1+1=3+1$

This simplifies to:

$\sqrt{5x-2}=4$

Squaring Both Sides

To get rid of the square root, we can square both sides of the equation.

$(\sqrt{5x-2})^2=4^2$

This simplifies to:

$5x-2=16$

Solving for $x$

Now, we can solve for $x$ by adding $2$ to both sides of the equation and then dividing both sides by $5$.

$5x-2+2=16+2$

This simplifies to:

$5x=18$

Dividing both sides by $5$ gives:

$x=\frac{18}{5}$

Conclusion

In this article, we have solved the equation $\sqrt{5x-2}-1=3$ to find the value of $x$. The solution to the equation is $x=\frac{18}{5}$. This is an essential skill in mathematics, and it is used to find the value of unknown variables in various equations.

Discussion

The solution to the equation is $x=\frac{18}{5}$. This is the correct answer among the options provided. The other options are $x=\frac{4}{5}$, $x=\frac{14}{5}$, and $x=\frac{6}{5}$. These options are incorrect, and they do not satisfy the equation.

Why is the Solution Correct?

The solution is correct because it satisfies the equation. When we substitute $x=\frac{18}{5}$ into the original equation, we get:

$\sqrt{5(\frac{18}{5})-2}-1=3$

This simplifies to:

$\sqrt{18-2}-1=3$

This further simplifies to:

$\sqrt{16}-1=3$

This simplifies to:

$4-1=3$

This is true, and it confirms that the solution is correct.

What is the Importance of Solving Equations?

Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. Equations are used to represent relationships between variables, and solving them is used to understand these relationships. Solving equations is used in various fields such as science, engineering, economics, and finance.

How to Solve Equations?

To solve equations, we need to follow a series of steps. The first step is to isolate the variable. This involves adding or subtracting terms to get rid of negative terms. The next step is to square both sides of the equation to get rid of the square root. Finally, we can solve for the variable by adding or subtracting terms and then dividing both sides by the coefficient of the variable.

Final Thoughts

In conclusion, solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. The solution to the equation $\sqrt{5x-2}-1=3$ is $x=\frac{18}{5}$. This is the correct answer among the options provided. Solving equations is used in various fields such as science, engineering, economics, and finance. It is an essential skill that is used to understand relationships between variables.

Frequently Asked Questions

• What is the solution to the equation $\sqrt{5x-2}-1=3$?
• How to solve equations?
• What is the importance of solving equations?

Answers

• The solution to the equation $\sqrt{5x-2}-1=3$ is $x=\frac{18}{5}$.
• To solve equations, we need to follow a series of steps. The first step is to isolate the variable. This involves adding or subtracting terms to get rid of negative terms. The next step is to square both sides of the equation to get rid of the square root. Finally, we can solve for the variable by adding or subtracting terms and then dividing both sides by the coefficient of the variable.
• Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. It is used in various fields such as science, engineering, economics, and finance.
  

Introduction

Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. In this article, we will answer some frequently asked questions about solving equations.

Q&A

Q1: What is the solution to the equation $\sqrt{5x-2}-1=3$?

A1: The solution to the equation $\sqrt{5x-2}-1=3$ is $x=\frac{18}{5}$.

Q2: How to solve equations?

A2: To solve equations, we need to follow a series of steps. The first step is to isolate the variable. This involves adding or subtracting terms to get rid of negative terms. The next step is to square both sides of the equation to get rid of the square root. Finally, we can solve for the variable by adding or subtracting terms and then dividing both sides by the coefficient of the variable.

Q3: What is the importance of solving equations?

A3: Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. It is used in various fields such as science, engineering, economics, and finance.

Q4: How to isolate the variable in an equation?

A4: To isolate the variable in an equation, we need to add or subtract terms to get rid of negative terms. This involves moving all the terms with the variable to one side of the equation and all the constant terms to the other side.

Q5: What is the difference between a linear equation and a quadratic equation?

A5: A linear equation is an equation in which the highest power of the variable is 1. A quadratic equation is an equation in which the highest power of the variable is 2.

Q6: How to solve a quadratic equation?

A6: To solve a quadratic equation, we need to use the quadratic formula. The quadratic formula is given by:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Q7: What is the significance of the quadratic formula?

A7: The quadratic formula is used to solve quadratic equations. It is a powerful tool that is used to find the solutions to quadratic equations.

Q8: How to check if a solution is correct?

A8: To check if a solution is correct, we need to substitute the solution into the original equation and check if it is true.

Q9: What is the importance of checking solutions?

A9: Checking solutions is an essential step in solving equations. It ensures that the solution is correct and that it satisfies the equation.

Q10: How to use a calculator to solve equations?

A10: To use a calculator to solve equations, we need to enter the equation into the calculator and then press the "solve" button. The calculator will then give us the solution to the equation.

Conclusion

In this article, we have answered some frequently asked questions about solving equations. Solving equations is an essential skill in mathematics, and it is used to find the value of unknown variables in various equations. We have discussed the importance of solving equations, how to isolate the variable, and how to use the quadratic formula to solve quadratic equations. We have also discussed the significance of checking solutions and how to use a calculator to solve equations.

Discussion

Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. In this article, we have discussed some frequently asked questions about solving equations. We have also discussed the importance of solving equations, how to isolate the variable, and how to use the quadratic formula to solve quadratic equations.

Why is Solving Equations Important?

Solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. It is used in various fields such as science, engineering, economics, and finance.

How to Use Solving Equations in Real-Life Situations?

Solving equations is used in various real-life situations. For example, it is used to find the value of unknown variables in scientific equations, to solve engineering problems, and to make financial decisions.

What are the Benefits of Solving Equations?

Solving equations has several benefits. It helps us to understand the relationships between variables, to make informed decisions, and to solve complex problems.

How to Practice Solving Equations?

To practice solving equations, we need to solve a variety of equations. We can start with simple equations and then move on to more complex equations. We can also use online resources and calculators to practice solving equations.

Final Thoughts

In conclusion, solving equations is an essential skill in mathematics. It is used to find the value of unknown variables in various equations. We have discussed some frequently asked questions about solving equations, and we have also discussed the importance of solving equations, how to isolate the variable, and how to use the quadratic formula to solve quadratic equations. We have also discussed the significance of checking solutions and how to use a calculator to solve equations.