Make { X $}$ The Subject Of:${ X - Qx = 2 }$

Mar 9, 2025 by ADMIN 46 views

**Solving for x in a Linear Equation**

Introduction

In algebra, solving for the subject of a linear equation is a fundamental concept that helps us understand the relationship between variables. In this article, we will focus on solving for x in the equation $x - qx = 2$ . This equation involves a variable x and a constant q, and our goal is to isolate x and make it the subject of the equation.

Understanding the Equation

The given equation is $x - qx = 2$ . To solve for x, we need to isolate x on one side of the equation. The equation involves a subtraction operation, which means we need to get rid of the term $-qx$ to isolate x.

Step 1: Add qx to Both Sides

To get rid of the term $-qx$ , we can add $qx$ to both sides of the equation. This will help us eliminate the negative term and make it easier to isolate x.

$x - qx + qx = 2 + qx$

By adding $qx$ to both sides, we get:

$x = 2 + qx$

Step 2: Subtract qx from Both Sides

Now that we have $x = 2 + qx$ , we need to get rid of the term $qx$ to isolate x. We can do this by subtracting $qx$ from both sides of the equation.

$x - qx = 2$

Subtracting $qx$ from both sides gives us:

$x = 2$

Solving for x

Now that we have $x = 2$ , we can say that the value of x is 2. This means that when we substitute x = 2 into the original equation, the equation holds true.

Conclusion

In this article, we solved for x in the equation $x - qx = 2$ . We used algebraic manipulation to isolate x and make it the subject of the equation. By adding $qx$ to both sides and then subtracting $qx$ from both sides, we were able to solve for x and find its value.

Tips and Tricks

When solving for x, always try to isolate x on one side of the equation.
Use algebraic manipulation to get rid of terms that are not necessary to isolate x.
Make sure to check your work by substituting the value of x back into the original equation.

Real-World Applications

Solving for x in a linear equation has many real-world applications. For example, in physics, we use linear equations to model the motion of objects. In economics, we use linear equations to model the relationship between variables such as supply and demand.

Common Mistakes

Not isolating x on one side of the equation.
Not using algebraic manipulation to get rid of unnecessary terms.
Not checking work by substituting the value of x back into the original equation.

Practice Problems

Solve for x in the equation $x + 3x = 5$ .
Solve for x in the equation $2x - 4x = 3$ .
Solve for x in the equation $x - 2x = 1$ .

Answer Key

$x = 1$
$x = -3$
$x = -1$

Conclusion

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (x) is 1. In other words, it is an equation that can be written in 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 following characteristics:

The highest power of the variable (x) is 1.
The equation can be written in the form ax + b = c.
The equation does not involve any exponents or roots.

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 (x) is 1, while a quadratic equation is an equation in which the highest power of the variable (x) is 2. For example, the equation x + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I solve for x in a linear equation?

A: To solve for x in a linear equation, follow these steps:

Isolate the variable (x) on one side of the equation.
Use algebraic manipulation to get rid of any terms that are not necessary to isolate x.
Check your work by substituting the value of x back into the original equation.

Q: What is the order of operations when solving for x in a linear equation?

A: When solving for x in a linear equation, follow the order of operations (PEMDAS):

Parentheses: Evaluate any expressions inside parentheses.
Exponents: Evaluate any exponents (such as squaring or cubing).
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to solve for x in a linear equation?

A: Yes, you can use a calculator to solve for x in a linear equation. However, it's always a good idea to check your work by substituting the value of x back into the original equation to ensure that the equation holds true.

Q: What are some common mistakes to avoid when solving for x in a linear equation?

A: Some common mistakes to avoid when solving for x in a linear equation include:

Not isolating the variable (x) on one side of the equation.
Not using algebraic manipulation to get rid of unnecessary terms.
Not checking work by substituting the value of x back into the original equation.

Q: How can I practice solving for x in linear equations?

A: You can practice solving for x in linear equations by working through example problems, such as those found in a math textbook or online resource. You can also try creating your own problems and solving them to test your skills.

Q: What are some real-world applications of solving for x in linear equations?

A: Solving for x in linear equations has many real-world applications, including:

Physics: Solving for x in linear equations can help model the motion of objects.
Economics: Solving for x in linear equations can help model the relationship between variables such as supply and demand.
Engineering: Solving for x in linear equations can help design and optimize systems.

Conclusion

Solving for x in a linear equation is a fundamental concept in algebra. By following the steps outlined in this article and practicing regularly, you can become proficient in solving for x in linear equations. Remember to check your work by substituting the value of x back into the original equation to ensure that the equation holds true.