Proving the Equation 230 - 220 x 0.5 5! True

When faced with a complex mathematical equation like 230 - 220 x 0.5 5!, it is important to break it down methodically and verify the result step-by-step. This article will walk you through the process of proving this equation to be true, making use of fundamental arithmetic and factorial concepts.

Understanding the Equation

The given equation is:

230 - 220 × 0.5 5 !

Here, 230 - 220 x 0.5 must be evaluated and compared to the value of 5 factorial (5!) to determine if the equation holds true.

Step-by-Step Calculation

Left-Hand Side (LHS) Evaluation

First, we perform the multiplication within the equation:

220 × 0.5 110

Next, we substitute this value back into the original equation:

230 - 110

Finally, we subtract the two numbers:

230 - 110 120

Right-Hand Side (RHS) Evaluation

The right-hand side of the equation is the factorial of 5, which is calculated as:

5 !

5! 5 × 4 × 3 × 2 × 1

Step-by-step calculation of 5!:

5 × 4 20 20 × 3 60 60 × 2 120 120 × 1 120

Conclusion

After evaluating both the left-hand side and right-hand side of the equation, we find that:

230 - 220 × 0.5 120

and

5 ! 120

Since both sides equal 120, the equation 230 - 220 x 0.5 5! is indeed true.

Further Exploration

The proof we have just carried out involves some basic arithmetic and the concept of factorial. Here's a brief explanation of factorial:

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example:

5 ! 5 × 4 × 3 × 2 × 1 120

Understanding factorial is crucial in solving various problems in combinatorics, probability, and other areas of mathematics.

Conclusion Summary

In summary, we demonstrated that 230 - 220 × 0.5 120 and 5! 120, thus proving the equation to be true. This step-by-step methodology can be applied to resolve similar complex equations and enhance your understanding of mathematical operations and factorial calculations.