## Unveiling the Value of X: Solving for X in 8x - 2y = 48

**What is the value of x in the equation 8x – 2y = 48, when y = 4?** This question delves into the realm of algebraic equations, where we aim to isolate and determine the value of an unknown variable, 'x', given a specific value for another variable, 'y'.

*Editor Note: This article explores solving for 'x' in the linear equation 8x – 2y = 48 with a specific value of 'y'. Learn how to utilize substitution to arrive at the correct value of 'x' and understand the importance of understanding linear equations in mathematics.*

Understanding the value of 'x' in this equation is crucial for various mathematical and scientific applications. From calculating the length of a side in a geometric shape to determining the quantity of a certain substance in a chemical reaction, the ability to solve for unknown variables is fundamental.

**Analysis:** To solve for 'x', we will embark on a step-by-step process using the given information. This guide will demonstrate the application of substitution and basic algebraic principles to arrive at the solution.

**Key Takeaways of Solving for 'x' in a Linear Equation**

Step | Explanation |
---|---|

1. Identify the given values. |
We are given the equation 8x - 2y = 48 and the value of y = 4. |

2. Substitute the known value. |
Replace the 'y' in the equation with its given value, 4. This gives us 8x - 2(4) = 48. |

3. Simplify the equation. |
Multiply 2 and 4 to get 8. The equation now becomes 8x - 8 = 48. |

4. Isolate the variable 'x'. |
Add 8 to both sides of the equation to get rid of the constant term on the left side. This gives us 8x = 56. |

5. Solve for 'x'. |
Finally, divide both sides of the equation by 8 to isolate 'x'. This leaves us with x = 7. |

**Understanding the Relationship between 'x' and 'y'**

**Equation:**The equation 8x - 2y = 48 represents a linear relationship between 'x' and 'y'. This means that for every change in 'y', there is a corresponding change in 'x' that maintains the equality.**Substitution:**The substitution of a specific value for 'y' allowed us to transform the equation into a simple linear equation with a single variable ('x').**Solution:**The solution x = 7 represents the specific value of 'x' that satisfies the equation when y = 4.

**Solving for 'x' in a Linear Equation**

**Substitution:**This method involves replacing one or more variables in an equation with their known values. It simplifies the equation and allows us to solve for the unknown variable.**Combining Like Terms:**This involves grouping together similar terms in the equation, often after applying substitution.**Inverse Operations:**This process utilizes the opposite mathematical operation to isolate the unknown variable. For instance, if we have 'x + 5', we would subtract 5 from both sides to isolate 'x'.

**Understanding the Concept of Linear Equations**

**Definition:**Linear equations are mathematical expressions that represent a straight line when graphed. They are characterized by a constant rate of change and a linear relationship between variables.**Applications:**Linear equations have wide-ranging applications in various fields, including physics, economics, engineering, and computer science. They are used to model real-world phenomena and solve problems involving relationships between variables.

**FAQ**

**Q: What happens if we change the value of 'y'?****A:**The value of 'x' will also change accordingly to maintain the equality in the equation.

**Q: Can we solve for 'y' if we know the value of 'x'?****A:**Yes, we can use the same substitution method to solve for 'y' if we know the value of 'x'.

**Q: What are other methods to solve for 'x' in a linear equation?****A:**Other methods include elimination and graphing.

**Tips for Solving Linear Equations**

**Understand the equation:**Carefully analyze the equation to identify the variables, constants, and their relationships.**Isolate the variable:**Use inverse operations to move all terms related to the unknown variable to one side of the equation.**Simplify the equation:**Combine like terms and simplify the expression as much as possible.**Check your solution:**Substitute the obtained value back into the original equation to verify if it satisfies the equality.

**Conclusion: The Power of Linear Equations**

The solution, x = 7, demonstrates the fundamental principle of solving linear equations and its significance in various fields. By understanding the relationship between variables, applying basic algebraic operations, and mastering the art of substitution, we can unlock the secrets behind equations and unravel the values of unknown variables. Linear equations are a powerful tool for problem-solving, and mastering them empowers us to tackle a wide range of mathematical challenges.