Solving for X in Linear Equations: A Comprehensive Guide

When dealing with algebraic equations, one of the most common tasks is to solve for a particular variable. This can be especially useful when given additional information, such as the value of another variable. In this comprehensive guide, we will walk through a detailed example to find the value of x in the equation 8x - 2y 48 when y 4.

Understanding the Equation

Let's start by understanding the equation in question:

8x - 2y 48

This is a linear equation with two variables, x and y. To find the value of x, we need to know the value of y. In this case, we are given y 4.

Substituting the Given Value

We can now substitute the value of y into the equation:

8x - 2(4) 48

Let's simplify this step by-step:

First, perform the multiplication: 8x - 8 48 Next, isolate the variable x by adding 8 to both sides: 8x 56 Finally, solve for x by dividing both sides by 8: x 7

So, the value of x is 7.

Applying the BIDMAS Rule

To ensure that our solution is accurate, let's follow the BIDMAS (Brackets, Indices, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)) rule:

8x - 2(4) 48

8x - 8 48 (Multiplication)

8x 56 (Addition)

x 7 (Division)

This confirms that our solution is correct.

Another Example

Let's solve another similar equation to reinforce the concept:

8x - 2y 48 when y 4

8x - 2(4) 48

8x - 8 48

8x 56

x 7

Again, the value of x is 7.

Conclusion

In this guide, we've provided a step-by-step process for solving the equation 8x - 2y 48 when y is given as 4. By substituting the known value, simplifying, and dividing, we found that x equals 7. This method can be applied to similar linear equations, making it a valuable skill in algebra.

Now you can confidently solve such equations on your own!