Question
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Tutor-Verified Answer
Answer
There is no solution to the equation.
Solution
1. Start with the equation:
\[
5x - 4 = 5(x+2)
\]
2. Distribute \(5\) on the right-hand side:
\[
5x - 4 = 5x + 10
\]
3. Subtract \(5x\) from both sides to eliminate the \(x\)-terms:
\[
5x - 4 - 5x = 5x + 10 - 5x \quad \Longrightarrow \quad -4 = 10
\]
4. Since \(-4 \ne 10\), the equation leads to a contradiction. Therefore, there is no solution.
The equation has no solution.
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Simplify this solution The Deep Dive
Let’s dive into solving the equation \( 5x - 4 = 5(x + 2) \). First, distribute the 5 on the right side: \[ 5x - 4 = 5x + 10. \] Next, subtract \( 5x \) from both sides to simplify: \[ -4 = 10. \] Oops! It looks like we have a contradiction! Since \(-4\) does not equal \(10\), this means that there are no solutions for this equation—essentially, it’s an inconsistent equation. Fun fact: this happens when both sides simplify to completely different values, indicating the lines represented by the equations would never intersect!
