I saw this question on a Facebook page and decided to share the solution with you all here. It might seem very simple, but if you're not careful, you might not get the correct answer. Take a moment to carefully read the question again.
Question:
Given that \(2x+4=12\), find the value of \(x!\)
Solution
Let's solve it step by step, explaining each part thoroughly.
Step 1: Understand the Problem
The given equation, \(2x+4=12\), is a straightforward linear equation. Our goal is to:
- Solve for \(x\) by isolating it in the equation.
- Calculate \(x!\), which represents the factorial of \(x\).
Quick Refresher in Factorials
The factorial of a number, denoted as \(x!\), is the product of all positive integers from 1 to \(x\). For example:
- \(4!=4\times3\times2\times1=24\).
- \(5!=5\times4\times3\times2\times1=120\).
If \(x=0\), by definition, \(0!=1\).
Now that we know what factorials are, let's solve the equation step by step.
Step 2: Solve for \(x\)
We start with the equation: \(2x+4=12\)
Step-by-step Solution:
Subtract 4 from both sides of the equation to simplify:
\(2x+4-4=12-4\)
\(2x=8\)
Divide both sides by 2 to isolate \(x\):
\(\frac{2x}{2}=\frac{8}{2}\)
\(x=4\)
Now we know that \(x=4\)
Step 3: Calculate \(x!\)
With \(x=4\), we need to calculate \(4!\)
\(4!=4\times3\times2\times1=24\)
\(\therefore x!=24\)
If there is a part you do not understand, feel free to use the comment section below to ask your question.