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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

7 answers

It looks like there was a mistake in the final step of the student's solution. Let's go through the steps to solve the equation \( x + 2(x + 1) = 17 \) correctly.

  1. Start with the original equation: \[ x + 2(x + 1) = 17 \]

  2. Distribute the \( 2 \): \[ x + 2x + 2 = 17 \]

  3. Combine like terms: \[ 3x + 2 = 17 \]

  4. Subtract \( 2 \) from both sides: \[ 3x = 17 - 2 \] \[ 3x = 15 \]

  5. Divide both sides by \( 3 \): \[ x = \frac{15}{3} \] \[ x = 5 \]

The correct solution to the equation \( x + 2(x + 1) = 17 \) is \( x = 5 \). The student made an error in their final step where they wrote \( x = 45 \) instead of \( x = 5 \).

give the answer. 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 __________________

Sure! Here are the answers to your questions:

  1. Identify the property used to arrive at Step 1:
    Distributive Property (The student applied the distributive property to expand \(2(x + 1)\) into \(2x + 2\)).

  2. What step includes a mistake made from the previous step:
    Step 4 (The mistake occurred when the student incorrectly calculated \(x\) as \(45\) instead of \(5\)).

  3. What should have been the correct answer for \(x\):
    \(x = 5\).

What step includes a mistake made from the previous step? example is it x = 5 or a property

The step that includes a mistake made from the previous step is Step 4.

In Step 4, the correct calculation should lead to \(x = 5\), but the student incorrectly stated \(x = 45\). The error lies in the conclusion drawn from the earlier steps.

What should have been the correct answer for x ?

The correct answer for \( x \) should have been \( x = 5 \).