Asked by Ame
this problem was solved incorrectly, solve the problem correctly then explain the error made:
3x + 2x - 6 = 24
-2x -2x
x - 6 = 24
+6 +6
x = 30
3x + 2x - 6 = 24
-2x -2x
x - 6 = 24
+6 +6
x = 30
Answers
Answered by
GPT-4o mini
Let's solve the equation correctly step by step.
The original equation is:
\[ 3x + 2x - 6 = 24 \]
1. First, combine like terms on the left side:
\[ (3x + 2x) - 6 = 24 \]
\[ 5x - 6 = 24 \]
2. Next, add 6 to both sides to isolate the term with \(x\):
\[ 5x - 6 + 6 = 24 + 6 \]
\[ 5x = 30 \]
3. Now, divide both sides by 5 to solve for \(x\):
\[ x = \frac{30}{5} \]
\[ x = 6 \]
So the correct solution is \(x = 6\).
### Explanation of the Error:
1. The first error occurs in the step where \(-2x - 2x\) was performed. It appears the equations were either incorrectly manipulated or miswritten.
2. The subsequent step where \(x - 6 = 24\) was written is incorrect; it seems to have dropped some terms and made an arbitrary simplification that did not follow the rules of algebra.
3. The final calculation mistakenly suggested adding 6 to both sides to get \(x = 30\) instead of recognizing that \(5x = 30\) must be divided by 5 to find \(x\).
The proper steps consistently follow arithmetic operations, and the use of parentheses to ensure each step is clear and accurate would help avoid such errors.
The original equation is:
\[ 3x + 2x - 6 = 24 \]
1. First, combine like terms on the left side:
\[ (3x + 2x) - 6 = 24 \]
\[ 5x - 6 = 24 \]
2. Next, add 6 to both sides to isolate the term with \(x\):
\[ 5x - 6 + 6 = 24 + 6 \]
\[ 5x = 30 \]
3. Now, divide both sides by 5 to solve for \(x\):
\[ x = \frac{30}{5} \]
\[ x = 6 \]
So the correct solution is \(x = 6\).
### Explanation of the Error:
1. The first error occurs in the step where \(-2x - 2x\) was performed. It appears the equations were either incorrectly manipulated or miswritten.
2. The subsequent step where \(x - 6 = 24\) was written is incorrect; it seems to have dropped some terms and made an arbitrary simplification that did not follow the rules of algebra.
3. The final calculation mistakenly suggested adding 6 to both sides to get \(x = 30\) instead of recognizing that \(5x = 30\) must be divided by 5 to find \(x\).
The proper steps consistently follow arithmetic operations, and the use of parentheses to ensure each step is clear and accurate would help avoid such errors.