Questions: Error Analysis: Multi-Step Equations Directions: Read the problem below. The problem was solved incorrectly. Find the error that was made and explain it. Then answer the problem correctly. Solve: 3x-4+2(x-5)=9x+8-2x Student Work: 3x-4+2(x-5)=9x+8-2x 3x-4+2x-10=7x+8 5x-6=7x+8 +6 5x=7x+14 -7x-7x -2x/-2=14/-2 x =-7

Error Analysis: Multi-Step Equations Directions: Read the problem below. The problem was solved incorrectly. Find the error that was made and explain it. Then answer the problem correctly. Solve: 3x-4+2(x-5)=9x+8-2x Student Work: 3x-4+2(x-5)=9x+8-2x 3x-4+2x-10=7x+8 5x-6=7x+8 +6 5x=7x+14 -7x-7x -2x/-2=14/-2 x =-7
Transcript text: Error Analysis: Multi-Step Equations Directions: Read the problem below. The problem was solved incorrectly. Find the error that was made and explain it. Then answer the problem correctly. Solve: $3 x-4+2(x-5)=9 x+8-2 x$ Student Work: $3 x-4+2(x-5)=9 x+8-2 x$ $3 x-4+2 x-10=7 x+8$ $5 x-6=7 x+8$ +6 $5 x=7 x+14$ $-7 x-7 x$ $\frac{-2 x}{-2}=\frac{14}{-2}$ x $=-7$
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Solution

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Solution Steps

To solve the given equation, we need to simplify both sides by distributing and combining like terms. Then, isolate the variable x by moving all terms involving x to one side of the equation and constants to the other side. Finally, solve for x by dividing both sides by the coefficient of x.

Step 1: Identify the mistake

The mistake made by the student was in simplifying the equation incorrectly.

Step 2: Correct the mistake

Starting from the original equation: \[3x - 4 + 2(x - 5) = 9x + 8 - 2x\] Expanding the terms: \[3x - 4 + 2x - 10 = 9x + 8 - 2x\] \[5x - 14 = 7x + 8\]

Step 3: Solve for x

Moving all terms involving x to one side: \[5x - 7x = 8 + 14\] \[-2x = 22\] \[x = -\frac{22}{2}\] \[x = -11\]

Final Answer

\[\boxed{x = -11}\]

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