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Given that \(2x+4=12\), find \(x!\)

 

Given that 2x+4=12, find the value of x!

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:

  1. Solve for \(x\) by isolating it in the equation.
  2. 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.

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