Solve For \[$ X \$\]:$\[ 5x + 2 = Cx + D \\]

**Solve for $x$: $5x + 2 = cx + d$** =====================================

Introduction

In this article, we will be solving a linear equation of the form $5x + 2 = cx + d$. This type of equation is a fundamental concept in algebra and is used to solve for the value of a variable, in this case, $x$. We will break down the steps to solve for $x$ and provide examples to illustrate the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form $ax + b = cx + d$, where $a$, $b$, $c$, and $d$ are constants, and $x$ is the variable.

How to Solve for $x$

To solve for $x$, we need to isolate the variable $x$ on one side of the equation. We can do this by using the following steps:

Step 1: Subtract $cx$ from both sides

Subtracting $cx$ from both sides of the equation will help us to get all the terms with $x$ on one side of the equation.

5x + 2 = cx + d
5x - cx = d - 2
(5-c)x = d - 2

Step 2: Divide both sides by $(5-c)$

Now that we have the term with $x$ on one side of the equation, we can divide both sides by $(5-c)$ to solve for $x$.

(5-c)x = d - 2
x = \frac{d - 2}{5-c}

Example 1: Solve for $x$

Let's use the equation $5x + 2 = 3x + 4$ to solve for $x$.

5x + 2 = 3x + 4
5x - 3x = 4 - 2
2x = 2
x = \frac{2}{2}
x = 1

Example 2: Solve for $x$

Let's use the equation $2x + 3 = 5x + 2$ to solve for $x$.

2x + 3 = 5x + 2
2x - 5x = 2 - 3
-3x = -1
x = \frac{-1}{-3}
x = \frac{1}{3}

Conclusion

Solving for $x$ in a linear equation is a straightforward process that involves isolating the variable $x$ on one side of the equation. By following the steps outlined above, we can solve for $x$ in any linear equation of the form $ax + b = cx + d$. We hope this article has provided a clear understanding of how to solve for $x$ and has helped to build your algebra skills.

Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1.

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

A: To solve for $x$, you need to isolate the variable $x$ on one side of the equation. You can do this by subtracting $cx$ from both sides and then dividing both sides by $(5-c)$.

Q: What if the equation has a fraction?

A: If the equation has a fraction, you can multiply both sides by the denominator to eliminate the fraction.

Q: Can I use a calculator to solve for $x$?

A: Yes, you can use a calculator to solve for $x$. However, it's always a good idea to check your work by plugging the solution back into the original equation.

Q: What if I get a negative value for $x$?

A: If you get a negative value for $x$, it means that the solution is not valid. You should check your work and make sure that you have isolated the variable $x$ correctly.

Additional Resources

If you need additional help or resources to solve for $x$, here are some additional resources that you can use:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

We hope this article has provided a clear understanding of how to solve for $x$ in a linear equation. If you have any further questions or need additional help, please don't hesitate to ask.