Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
Carlos solved the equation below for x using inverse operations. His solution is x = 6.5. What mistake did Carlos make and how...Question
Carlos solved the equation below for x using inverse operations. His solution is x = 6.5. What mistake did Carlos make and how could he have checked his solution to know for certain that his answer is correct?
5x + 7.5 = 25
5x = 32.5
x = 6.5
What mistake did Carlos make with the steps he took to solve for x? Explain in detail
5x + 7.5 = 25
5x = 32.5
x = 6.5
What mistake did Carlos make with the steps he took to solve for x? Explain in detail
Answers
There are no human answers yet.
Answered by
GPT-4o mini
Let's break down the solution Carlos attempted to find and analyze where he went wrong.
The original equation Carlos was tasked with solving is:
\[ 5x + 7.5 = 25 \]
**Step 1: Isolate the term with \(x\)**
Carlos aimed to isolate \(5x\) by subtracting \(7.5\) from both sides of the equation. The correct calculation should be:
\[ 5x + 7.5 - 7.5 = 25 - 7.5 \]
This simplifies to:
\[ 5x = 25 - 7.5 \]
\[ 5x = 17.5 \] (Not 32.5)
Carlos incorrectly concluded that \(5x = 32.5\), which was a mistake at this first step of isolating \(5x\).
**Step 2: Solve for \(x\)**
Next, he should have divided both sides by 5 to solve for \(x\):
\[ x = \frac{17.5}{5} \]
\[ x = 3.5 \] (Again, not 6.5)
**Carlos's Mistake Summary:**
1. Carlos incorrectly subtracted \(7.5\) from \(25\) and arrived at \(32.5\) instead of \(17.5\).
2. This fundamental miscalculation led to an incorrect value of \(x\).
**How Could He Have Checked His Solution?**
To verify the solution, Carlos could substitute his calculated value of \(x\) back into the original equation:
1. Substitute \(x = 6.5\) into the original equation \(5x + 7.5\):
\[
5(6.5) + 7.5 = 32.5 + 7.5 = 40
\]
The left side equals \(40\), but the original equation states it should equal \(25\).
Since the numbers do not match, Carlos would realize that \(x = 6.5\) is not a valid solution.
Instead, if he checked by substituting \(x = 3.5\):
\[
5(3.5) + 7.5 = 17.5 + 7.5 = 25
\]
The left side equals \(25\), confirming that \(x = 3.5\) is the correct solution.
In conclusion, Carlos's mistake was in incorrectly simplifying \(25 - 7.5\), and a way to avoid such mistakes is to always check the results by substituting the solution back into the original equation.
The original equation Carlos was tasked with solving is:
\[ 5x + 7.5 = 25 \]
**Step 1: Isolate the term with \(x\)**
Carlos aimed to isolate \(5x\) by subtracting \(7.5\) from both sides of the equation. The correct calculation should be:
\[ 5x + 7.5 - 7.5 = 25 - 7.5 \]
This simplifies to:
\[ 5x = 25 - 7.5 \]
\[ 5x = 17.5 \] (Not 32.5)
Carlos incorrectly concluded that \(5x = 32.5\), which was a mistake at this first step of isolating \(5x\).
**Step 2: Solve for \(x\)**
Next, he should have divided both sides by 5 to solve for \(x\):
\[ x = \frac{17.5}{5} \]
\[ x = 3.5 \] (Again, not 6.5)
**Carlos's Mistake Summary:**
1. Carlos incorrectly subtracted \(7.5\) from \(25\) and arrived at \(32.5\) instead of \(17.5\).
2. This fundamental miscalculation led to an incorrect value of \(x\).
**How Could He Have Checked His Solution?**
To verify the solution, Carlos could substitute his calculated value of \(x\) back into the original equation:
1. Substitute \(x = 6.5\) into the original equation \(5x + 7.5\):
\[
5(6.5) + 7.5 = 32.5 + 7.5 = 40
\]
The left side equals \(40\), but the original equation states it should equal \(25\).
Since the numbers do not match, Carlos would realize that \(x = 6.5\) is not a valid solution.
Instead, if he checked by substituting \(x = 3.5\):
\[
5(3.5) + 7.5 = 17.5 + 7.5 = 25
\]
The left side equals \(25\), confirming that \(x = 3.5\) is the correct solution.
In conclusion, Carlos's mistake was in incorrectly simplifying \(25 - 7.5\), and a way to avoid such mistakes is to always check the results by substituting the solution back into the original equation.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.