which interval is the solution set to $0.35x - 4.8

Question

which interval is the solution set to $0.35x - 4.8 < 5.2 - 0.9x$?

$(-\infty, 8)$

$(-\infty, -8)$

$(-8, \infty)$

$(8, \infty)$

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": [ "Solving Linear Inequalities", "Interval Notation" ], "new_concepts": [], "current_concepts": [ "Solving Linear Inequalities", "Interval Notation" ] } ## Collect variable terms Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 0.35x - 4.8 &< 5.2 - 0.9x \ 0.35x + 0.9x - 4.8 &< 5.2 \ 1.25x - 4.8 &< 5.2 \end{aligned} $$ ## Isolate variable term Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 1.25x &< 5.2 + 4.8 \ 1.25x &< 10 \end{aligned} $$ ## Solve for x Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} x &< \frac{10}{1.25} \ x &< 8 \end{aligned} $$ ## Convert to interval notation Using the *Interval Notation* knowledge point $$ x \in (-\infty, 8) $$

(A) $(-\infty, 8)$

(B) $(-\infty, -8)$

(C) $(-8, \infty)$

(D) $(8, \infty)$

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

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Question

Explanation:

Collect variable terms

Isolate variable term

Solve for x

Convert to interval notation

Answer: