Math  /  Algebra

Question1. Two students both solved the equation 4(x0.5)=6-4(x-0.5)=6 incorrectly. The work of each student is shown.
Student A's Work: 4(x0.5)=6-4(x-0.5)=6
Step 1: 4x2=6-4 x-2=6 Step 2: 4x=8-4 x=8 Step 3: x=2x=-2 Student B's Work: 4(x0.5)=6-4(x-0.5)=6
Step 1: 4x+2=6-4 x+2=6 Step 2: 4x=8-4 x=8 Step 3: x=2x=-2 In which step of their work did Student A and Student B make their first mistake? A Student A made their first mistake in Step 1 and Student B made their first mistake in Step 1. B Student A made their first mistake in Step 1 and Student B made their first mistake in Step 2. C Student A made their first mistake in Step 2 and Student B made their first mistake in Step 1. D Student A made their first mistake in Step 2 and Student B made their first mistake in Step 2

Studdy Solution

STEP 1

1. The original equation is 4(x0.5)=6 -4(x-0.5)=6 .
2. We need to identify the first mistake in each student's solution process.

STEP 2

1. Analyze Student A's work to identify the first mistake.
2. Analyze Student B's work to identify the first mistake.
3. Determine the correct answer choice based on the analysis.

STEP 3

Analyze Student A's Step 1: - The original equation is 4(x0.5)=6 -4(x-0.5)=6 . - Distribute 4-4 to both terms inside the parentheses: 4×x=4x-4 \times x = -4x and 4×0.5=2-4 \times -0.5 = 2. - The correct transformation should be 4x+2=6-4x + 2 = 6.
Student A's Step 1: 4x2=6-4x - 2 = 6 is incorrect because the sign of the constant term is wrong.

STEP 4

Analyze Student B's Step 1: - The original equation is 4(x0.5)=6 -4(x-0.5)=6 . - Distribute 4-4 to both terms inside the parentheses: 4×x=4x-4 \times x = -4x and 4×0.5=2-4 \times -0.5 = 2. - The correct transformation should be 4x+2=6-4x + 2 = 6.
Student B's Step 1: 4x+2=6-4x + 2 = 6 is correct.

STEP 5

Analyze Student B's Step 2: - From the correct Step 1: 4x+2=6-4x + 2 = 6. - Subtract 2 from both sides: 4x=4-4x = 4.
Student B's Step 2: 4x=8-4x = 8 is incorrect because the subtraction was done incorrectly.
The correct answer choice is:
C Student A made their first mistake in Step 1 and Student B made their first mistake in Step 2.

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