Solve For { X $}$ In The Equation:${ \frac{1}{5}x - 2 = 4 }$

Mar 10, 2025 by ADMIN 62 views

$Solve for ${ x }$ in the Equation: ${\frac{1}{5}x - 2 = 4}$$

Introduction

Mathematics is a fundamental subject that plays a crucial role in our daily lives. It is used in various fields such as science, engineering, economics, and finance. One of the essential skills in mathematics is solving equations, which involves finding the value of a variable that satisfies a given equation. In this article, we will focus on solving a linear equation, specifically the equation ${\frac{1}{5}x - 2 = 4}$ . We will use algebraic methods to isolate the variable ${ x }$ and find its value.

Understanding the Equation

The given equation is a linear equation in one variable, ${ x }$ . It is in the form of ${\frac{1}{5}x - 2 = 4}$ , where ${\frac{1}{5}x}$ is the coefficient of ${ x }$ , and ${-2}$ is the constant term. Our goal is to solve for ${ x }$ , which means we need to isolate ${ x }$ on one side of the equation.

Step 1: Add 2 to Both Sides of the Equation

To isolate ${ x }$ , we need to get rid of the constant term, ${-2}$ . We can do this by adding ${2}$ to both sides of the equation. This will keep the equation balanced, as we are performing the same operation on both sides.

${\frac{1}{5}x - 2 + 2 = 4 + 2}$

Simplifying the equation, we get:

${\frac{1}{5}x = 6}$

Step 2: Multiply Both Sides by 5

Now that we have isolated the term with ${ x }$ , we need to get rid of the fraction. We can do this by multiplying both sides of the equation by ${5}$ . This will eliminate the fraction and give us a simpler equation.

${5 \times \frac{1}{5}x = 5 \times 6}$

Simplifying the equation, we get:

${x = 30}$

Conclusion

In this article, we solved the linear equation ${\frac{1}{5}x - 2 = 4}$ using algebraic methods. We added ${2}$ to both sides of the equation to isolate the term with ${ x }$ , and then multiplied both sides by ${5}$ to eliminate the fraction. This gave us the value of ${ x }$ , which is ${30}$ . Solving equations is an essential skill in mathematics, and it has numerous applications in real-life situations.

Applications of Solving Equations

Solving equations is a fundamental skill in mathematics that has numerous applications in various fields. Here are a few examples:

Science: In physics, equations are used to describe the motion of objects, the behavior of particles, and the properties of materials. Solving equations helps scientists understand the underlying principles of natural phenomena.
Engineering: In engineering, equations are used to design and optimize systems, structures, and processes. Solving equations helps engineers create efficient and effective solutions to complex problems.
Economics: In economics, equations are used to model economic systems, understand the behavior of markets, and make predictions about future trends. Solving equations helps economists make informed decisions about economic policy.
Finance: In finance, equations are used to calculate interest rates, investment returns, and risk management strategies. Solving equations helps financial analysts make informed decisions about investments and risk management.

Tips for Solving Equations

Solving equations can be challenging, but with practice and patience, anyone can master this skill. Here are a few tips to help you solve equations:

Read the equation carefully: Before starting to solve an equation, read it carefully to understand what is being asked. Identify the variable, the coefficients, and the constant term.
Use algebraic methods: Algebraic methods, such as addition, subtraction, multiplication, and division, are essential for solving equations. Use these methods to isolate the variable and solve for its value.
Check your work: Once you have solved an equation, check your work to ensure that the solution is correct. Plug the solution back into the original equation to verify that it is true.
Practice, practice, practice: Solving equations is a skill that requires practice to develop. Practice solving equations regularly to build your confidence and improve your skills.

Conclusion

Solving equations is a fundamental skill in mathematics that has numerous applications in various fields. By following the steps outlined in this article, you can solve linear equations and develop your algebraic skills. Remember to read the equation carefully, use algebraic methods, check your work, and practice regularly to become proficient in solving equations. With practice and patience, you can master this skill and apply it to real-life situations.

Introduction

Solving equations is a fundamental skill in mathematics that has numerous applications in various fields. In our previous article, we discussed how to solve a linear equation using algebraic methods. However, we understand that readers may have questions about solving equations. In this article, we will address some of the most frequently asked questions (FAQs) about solving equations.

Q: What is an equation?

A: An equation is a statement that expresses the equality of two mathematical expressions. It consists of a variable, coefficients, and a constant term. For example, the equation ${2x + 3 = 5}$ is a statement that expresses the equality of the expressions ${2x + 3}$ and ${5}$ .

Q: What is a variable?

A: A variable is a symbol that represents a value that can change. In an equation, the variable is the unknown value that we are trying to solve for. For example, in the equation ${2x + 3 = 5}$ , the variable is ${x}$ .

Q: What is a coefficient?

A: A coefficient is a number that is multiplied by a variable. In an equation, the coefficient is the number that is multiplied by the variable. For example, in the equation ${2x + 3 = 5}$ , the coefficient of ${x}$ is ${2}$ .

Q: What is a constant term?

A: A constant term is a number that is not multiplied by a variable. In an equation, the constant term is the number that is not multiplied by the variable. For example, in the equation ${2x + 3 = 5}$ , the constant term is ${3}$ .

Q: How do I solve an equation?

A: To solve an equation, you need to isolate the variable on one side of the equation. You can do this by using algebraic methods such as addition, subtraction, multiplication, and division. For example, to solve the equation ${2x + 3 = 5}$ , you can subtract ${3}$ from both sides to get ${2x = 2}$ , and then divide both sides by ${2}$ to get ${x = 1}$ .

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when solving an equation. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I check my work?

A: To check your work, plug the solution back into the original equation to verify that it is true. For example, if you solved the equation ${2x + 3 = 5}$ and got ${x = 1}$ , you can plug ${x = 1}$ back into the original equation to get ${2(1) + 3 = 5}$ , which is true.

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

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

Not reading the equation carefully: Make sure to read the equation carefully to understand what is being asked.
Not using the correct order of operations: Make sure to follow the order of operations when solving an equation.
Not checking your work: Make sure to check your work by plugging the solution back into the original equation.
Not being careful with negative numbers: Be careful when working with negative numbers, as they can change the sign of the equation.

Conclusion

Solving equations is a fundamental skill in mathematics that has numerous applications in various fields. By understanding the basics of equations, variables, coefficients, and constant terms, you can solve equations using algebraic methods. Remember to follow the order of operations, check your work, and avoid common mistakes to become proficient in solving equations. With practice and patience, you can master this skill and apply it to real-life situations.