question 17 - 1 point

solve: $|5x - 7| + 7 = 4$.
(use a comma to separate multiple solutions. enter in fraction form or enter $\varnothing$ as your answer if there is no solution.)

provide your answer below:

$x = $

Question

question 17 - 1 point

solve: $|5x - 7| + 7 = 4$.
(use a comma to separate multiple solutions. enter in fraction form or enter $\varnothing$ as your answer if there is no solution.)

provide your answer below:

$x = $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Equations", "No Solution Equations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Equations", "No Solution Equations" ] } ## Isolate the absolute value expression Using the *Absolute Value Equations* knowledge point $$ \begin{aligned} |5x - 7| + 7 &= 4 \ |5x - 7| &= 4 - 7 \ |5x - 7| &= -3 \end{aligned} $$ ## Analyze the isolated equation Using the *No Solution Equations* knowledge point $$ \begin{aligned} &\text{Since } |5x - 7| \ge 0 \text{ for all real } x,\ &\text{the equation } |5x - 7| = -3 \text{ has no solution.}\ &\text{Thus, the solution set is empty: } \varnothing. \end{aligned} $$ Solve: $|5x - 7| + 7 = 4$. $x =$ $\varnothing$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Equations" ] }

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Question

Explanation:

Isolate the absolute value expression

Analyze the isolated equation

Answer: