Question
A student solved the equation: x+2(x+1)=17
Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
Step 1: x+2x+2=17
Step 2: 3x+2=17
Step 3: 3x=15
Step 4: x=45
Answers
Answered by
find
Identify the property used to arrive at Step 1 ______________________
What step includes a mistake made from the previous step______________
What should have been the correct answer for x __________________
Answered by
GPT-4o mini
It looks like there is an error in the solution process as presented. Let's go through the equation step by step to find the solution correctly.
The original equation is:
\[ x + 2(x + 1) = 17 \]
Step 1: Distribute the \(2\) in the expression:
\[ x + 2x + 2 = 17 \]
Step 2: Combine like terms:
\[ 3x + 2 = 17 \]
Step 3: Subtract \(2\) from both sides:
\[ 3x = 17 - 2 \]
\[ 3x = 15 \]
Step 4: Divide both sides by \(3\):
\[ x = \frac{15}{3} \]
\[ x = 5 \]
So, the correct solution to the equation \( x + 2(x + 1) = 17 \) is \( x = 5 \). The final answer \( x = 45 \) in the provided steps is incorrect.
The original equation is:
\[ x + 2(x + 1) = 17 \]
Step 1: Distribute the \(2\) in the expression:
\[ x + 2x + 2 = 17 \]
Step 2: Combine like terms:
\[ 3x + 2 = 17 \]
Step 3: Subtract \(2\) from both sides:
\[ 3x = 17 - 2 \]
\[ 3x = 15 \]
Step 4: Divide both sides by \(3\):
\[ x = \frac{15}{3} \]
\[ x = 5 \]
So, the correct solution to the equation \( x + 2(x + 1) = 17 \) is \( x = 5 \). The final answer \( x = 45 \) in the provided steps is incorrect.