Solving Equations: A Step-by-Step Guide to Solving 4x - 7 25

Solving algebraic equations is a fundamental skill in mathematics, and it is crucial for students and professionals alike. Today, we will guide you through the process of solving the linear equation 4x - 7 25, step by step. Each step will be explained clearly to help you understand the process.

Understanding the Equation

When you see an equation like 4x - 7 25, your goal is to isolate the variable x on one side of the equation. This can be achieved through a series of algebraic operations, which maintain the balance of the equation.

The Equation: 4x - 7 25

The given equation is:

4x - 7 25

Step 1: Isolate the Term with the Variable

The first step in solving the equation is to isolate the term that contains the variable x on one side of the equation. In this case, we want to get rid of the -7 on the left side so that we are left with just 4x. We do this by adding 7 to both sides of the equation. This is because adding the same value to both sides maintains the equality.

4x - 7 7 25 7

Simplifying this, we get:

4x 32

Step 2: Solve for x

Now that we have 4x 32, our next step is to isolate x. Since x is multiplied by 4, we need to divide both sides of the equation by 4 to get x alone on one side. Again, dividing both sides by the same value maintains the balance of the equation.

4x / 4 32 / 4

Simplifying this, we get:

x 8

Verification

To ensure our solution is correct, we can substitute x 8 back into the original equation and check if both sides are equal.

4x - 7 25

Substitute x 8:

4(8) - 7 25

32 - 7 25

25 25

This confirms that our solution is correct: the value of x that satisfies the equation 4x - 7 25 is indeed x 8.

Related Content

Understanding how to solve linear equations like 4x - 7 25 is the foundation for more advanced algebraic concepts. If you're interested in exploring more about solving equations, here are a few related topics:

Solving More Complex Equations Linear Equations in Real Life Algebraic Problem-Solving Techniques

By mastering the basics, you are paving the way for success in higher-level mathematics and real-world problem-solving. Keep practicing and you'll see improvement in your algebra skills!