3. solve $2x - 7 = 3x - 2(x + 8)$ for $x$.

$x = 9$

$x = -23$

$x = -9$

$x = 23$

Question

3. solve $2x - 7 = 3x - 2(x + 8)$ for $x$.

$x = 9$

$x = -23$

$x = -9$

$x = 23$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Algebraic Simplification", "Like Terms Identification" ], "new_concepts": [ "Linear Equation Solving" ], "current_concepts": [ "Algebraic Simplification", "Like Terms Identification", "Linear Equation Solving" ] } ## Distribute the constant on the right side Using the *Algebraic Simplification* knowledge point $$ \begin{aligned} 2x - 7 &= 3x - 2(x + 8) \ 2x - 7 &= 3x - 2x - 16 \end{aligned} $$ ## Combine like terms on the right side Using the *Like Terms Identification* knowledge point $$ \begin{aligned} 2x - 7 &= (3x - 2x) - 16 \ 2x - 7 &= x - 16 \end{aligned} $$ ## Isolate the variable terms Subtract $x$ from both sides to gather variables. $$ \begin{aligned} 2x - x - 7 &= -16 \ x - 7 &= -16 \end{aligned} $$ ## Solve for x Add $7$ to both sides to isolate $x$. $$ \begin{aligned} x &= -16 + 7 \ x &= -9 \end{aligned} $$

x = 9

x = -23

x = -9

x = 23

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

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QUESTION IMAGE

Question

Explanation:

Distribute the constant on the right side

Combine like terms on the right side

Isolate the variable terms

Solve for x

Answer: