Solving Equations to Find the Value of x

When dealing with algebraic equations, the primary goal is to solve for the unknown variable, typically denoted as x. This process involves a series of logical and arithmetic steps to isolate the variable on one side of the equation. In this article, we will walk through the process of solving an equation to find the value of x using a specific example.

Understanding the Equation

Consider the expression provided: 5x23x43x-2. At first glance, it might appear to be a sequence, but it is, in fact, an equation to be solved for x. The confusion may arise due to the similar notations used in sequences and equations. However, the correct form of the equation is:

5x253x4-2

Step-by-Step Solution Process

Let's solve this equation to find the value of x.

Step 1: Remove Fractions

Start by removing the fractions to simplify the equation. This can be accomplished by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. In this case, the LCM of 25 and 4 is 100.

5x253x4-2

Multiplying through by 100:

100×5x25100×3x4-2×100

Simplifies to:

275x-200

Step 2: Isolate the Variable

The next step is to isolate the variable x on one side of the equation. Begin by moving all terms with x to one side and constant terms to the other.

2-75x-200

Simplify:

-55x-200

Step 3: Solve for x

Finally, to find the value of x, divide both sides of the equation by the coefficient of x (which is -55).

x-200/-551

Simplify:

x20055

Further simplify:

x4011

Converting to decimal:

x-4

Conclusion

The value of x that satisfies the equation 5x253x4-2 is x -4.

This process of solving algebraic equations is a fundamental skill in mathematics. Understanding the steps involved in these processes helps ensure accuracy in solving more complex problems. For further assistance with solving algebraic equations, consider using online resources or seeking help from a mathematics tutor.