irene made a mistake when she solved this inequality.

step 1: $-6(x + 3) + 10

Question

irene made a mistake when she solved this inequality.

step 1: $-6(x + 3) + 10 < -2$
step 2: $-6x - 18 + 10 < -2$
step 3: $-6x - 8 < -2$
step 4: $-6x < 6$
step 5: $x < -1$

between which two consecutive steps did irene make a mistake?

step 1 and step 2
step 2 and step 3
step 3 and step 4
step 4 and step 5

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Properties of Inequality", "Solving Linear Inequalities" ], "new_concepts": [], "current_concepts": [ "Properties of Inequality", "Solving Linear Inequalities" ] } ## Analyze the algebraic transformations in each step $$ \begin{aligned} &\text{Step 1: } -6(x + 3) + 10 < -2 \ &\text{Step 2: } -6x - 18 + 10 < -2 \quad (\text{Correct distributive property}) \ &\text{Step 3: } -6x - 8 < -2 \quad (\text{Correct simplification: } -18 + 10 = -8) \ &\text{Step 4: } -6x < 6 \quad (\text{Correct addition property of inequality: } -2 + 8 = 6) \ &\text{Step 5: } x < -1 \quad (\text{Incorrect division by a negative number without reversing the inequality sign}) \end{aligned} $$ ## Identify the step containing the error $$ \begin{aligned} &-6x < 6 \ &x > -1 \quad (\text{Correct division by } -6) \end{aligned} $$ The error occurred between step 4 and step 5.

step 1 and step 2

step 2 and step 3

step 3 and step 4

step 4 and step 5

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Linear Inequalities" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the algebraic transformations in each step

Identify the step containing the error

Answer: