To solve the equation [tex]\(\frac{2x + 8}{2x + 4} = 1\)[/tex], let's follow a step-by-step approach:
1. Analyze the equation:
The given equation is:
[tex]\[
\frac{2x + 8}{2x + 4} = 1
\][/tex]
2. Eliminate the fraction by multiplying both sides by the denominator:
To get rid of the fraction, multiply both sides of the equation by [tex]\((2x + 4)\)[/tex] (assuming [tex]\(2x + 4 \neq 0\)[/tex]):
[tex]\[
2x + 8 = 1 \cdot (2x + 4)
\][/tex]
This simplifies to:
[tex]\[
2x + 8 = 2x + 4
\][/tex]
3. Simplify the equation:
Subtract [tex]\(2x\)[/tex] from both sides of the equation to isolate the constant terms:
[tex]\[
2x + 8 - 2x = 2x + 4 - 2x
\][/tex]
[tex]\[
8 = 4
\][/tex]
4. Determine the validity of the equation:
We see that [tex]\(8 = 4\)[/tex] is a false statement. Therefore, there is no value of [tex]\(x\)[/tex] that can satisfy the original equation.
Conclusion:
The equation [tex]\(\frac{2x + 8}{2x + 4} = 1\)[/tex] has no solution. The key step revealed a contradiction, indicating that no value of [tex]\(x\)[/tex] can make the equation true. Thus, the solution set is empty.
