Understanding the Equation 5x 3 - 3 - 7 3 and Solving for x

Equations are a fundamental part of algebra, and mastering them is essential for solving mathematical problems. In this article, we will explore the process of solving the equation 5x 3 - 3 - 7 3 for x, step by step. This process will help clear up any confusion and ensure a deep understanding of algebraic principles.

Solving 5x 3 - 3 - 7 3

The equation we are examining is 5x 3 - 3 - 7 3. Our goal is to isolate the variable x on one side of the equation. Let's break down the solution into manageable steps.

Step 1: Simplifying the Equation

First, let us simplify the left-hand side of the equation. Notice that 3 and -3 cancel each other out:

5x 3 - 3 - 7 3 5x - 7 3

Now, our equation is in a simpler form: 5x - 7 3.

Step 2: Isolating the Term with x

Next, we need to add 7 to both sides of the equation to isolate the term with x:

5x - 7 3 5x 3 7 5x 10

Now, the equation is simplified to 5x 10.

Step 3: Solving for x

To solve for x, we divide both sides of the equation by 5:

5x 10 x 10 / 5 x 2

Therefore, the value of x is 2.

Alternate Approaches to Solving the Equation

Let's explore a few alternative methods to solving the equation 5x 3 - 3 - 7 3:

Method 1: Using Like Terms

One common approach is to transfer like terms to each side of the equation. Here's how it is done:

5x 3 - 3 - 7 3 5x 3 - 3 - 7 3 5x 10 x 10 / 5 x 2

Method 2: Simplifying Expressions

Another way to solve the equation is to simplify the expressions step by step:

5x 3 - 3 - 7 3 5x - 7 3 5x 10 x 10 / 5 x 2

Method 3: Canceling Out Terms

You can also cancel out terms that are opposites, like the 3 and -3, directly: