List The Steps To Solve The Following Equation: 5 X − 6 = 44 5x - 6 = 44 5 X − 6 = 44 . Then Solve For X X X .

Mar 12, 2025 by ADMIN 111 views

**Solving Linear Equations: A Step-by-Step Guide**

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a simple linear equation of the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. We will use the equation $5x - 6 = 44$ as an example to illustrate the steps involved in solving a linear equation.

Understanding the Equation

Before we start solving the equation, let's understand what it represents. The equation $5x - 6 = 44$ is a linear equation in one variable, $x$ . The equation states that the product of $5$ and $x$ minus $6$ is equal to $44$ . Our goal is to isolate the variable $x$ and find its value.

Step 1: Add or Subtract Constants

The first step in solving a linear equation is to isolate the variable term on one side of the equation. In this case, we have a constant term, $-6$ , on the left-hand side of the equation. To eliminate this constant, we can add $6$ to both sides of the equation. This will not change the value of the equation, but it will simplify it.

# Original equation
# 5x - 6 = 44

Step 2: Divide or Multiply

Now that we have isolated the variable term, we can divide both sides of the equation by the coefficient of the variable, which is $5$ . This will give us the value of the variable.

# 5x = 50

Step 3: Check the Solution

Once we have found the value of the variable, we can plug it back into the original equation to check if it is true. If the equation holds true, then we have found the correct solution.

# Original equation
# 5x - 6 = 44

Conclusion

In this article, we have walked through the steps involved in solving a linear equation of the form $ax + b = c$ . We used the equation $5x - 6 = 44$ as an example to illustrate the process. By following these steps, we can solve linear equations and find the value of the variable.

Tips and Tricks

Always check the solution by plugging it back into the original equation.
Use the order of operations (PEMDAS) to simplify the equation.
Use algebraic properties, such as the distributive property, to simplify the equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes

Failing to check the solution by plugging it back into the original equation.
Not using the order of operations (PEMDAS) to simplify the equation.
Not using algebraic properties, such as the distributive property, to simplify the equation.

Conclusion

Introduction

In our previous article, we walked through the steps involved in solving a linear equation of the form $ax + b = c$ . In this article, we will answer some common questions that students and professionals may have when it comes to solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. In other words, it is an equation of the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the highest power of the variable. If the highest power is 1, then the equation is linear. For example, the equation $2x + 3 = 5$ is linear because the highest power of $x$ is 1.

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

A: A linear equation is an equation in which the highest power of the variable is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 2x + 1 = 0$ is a quadratic equation because the highest power of $x$ is 2.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, follow the same steps as you would for a linear equation without fractions. However, be sure to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when simplifying an expression. The acronym PEMDAS stands for:

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 use algebraic properties to simplify an equation?

A: Algebraic properties, such as the distributive property, can be used to simplify an equation by eliminating parentheses and combining like terms. For example, the equation $2(x + 3) = 10$ can be simplified using the distributive property as follows:

# 2(x + 3) = 10

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is an equation in which the highest power of the variable is 1, while a system of linear equations is a set of two or more linear equations that are solved simultaneously. For example, the system of linear equations:

# 2x + 3y = 5
# x - 2y = -3

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, follow these steps:

Write the system of linear equations.
Use the method of substitution or elimination to solve for one variable.
Substitute the value of the variable into one of the original equations to solve for the other variable.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, we can solve linear equations and find the value of the variable. Remember to always check the solution by plugging it back into the original equation, and use algebraic properties and the order of operations to simplify the equation.

Tips and Tricks

Always check the solution by plugging it back into the original equation.
Use the order of operations (PEMDAS) to simplify the equation.
Use algebraic properties, such as the distributive property, to simplify the equation.
Use the method of substitution or elimination to solve a system of linear equations.

Real-World Applications

Linear equations have numerous real-world applications, including:

Physics: Linear equations are used to describe the motion of objects under constant acceleration.
Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
Economics: Linear equations are used to model economic systems and make predictions about future trends.

Common Mistakes

Failing to check the solution by plugging it back into the original equation.
Not using the order of operations (PEMDAS) to simplify the equation.
Not using algebraic properties, such as the distributive property, to simplify the equation.
Not using the method of substitution or elimination to solve a system of linear equations.