which represents the solution set to the inequality \$5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)\$?

\$x > 2.5\$

\$(-2.5, \infty)\$

\$(-\infty, 2.5)\$

\$x < -2.5\$

Question

which represents the solution set to the inequality $5.1(3 + 2.2x) > -14.25 - 6(1.7x + 4)$?

$x > 2.5$

$(-2.5, \infty)$

$(-\infty, 2.5)$

$x < -2.5$

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", "Distributive Property", "Interval Notation" ], "new_concepts": [], "current_concepts": [ "Solving Linear Inequalities", "Distributive Property", "Interval Notation" ] } ## Expand both sides of the inequality Using the **Distributive Property** knowledge point $$ \begin{aligned} 5.1(3 + 2.2x) &> -14.25 - 6(1.7x + 4) \ 15.3 + 11.22x &> -14.25 - 10.2x - 24 \end{aligned} $$ ## Simplify the right side Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} 15.3 + 11.22x &> -38.25 - 10.2x \end{aligned} $$ ## Isolate the variable terms Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} 11.22x + 10.2x &> -38.25 - 15.3 \ 21.42x &> -53.55 \end{aligned} $$ ## Solve for x Using the **Solving Linear Inequalities** knowledge point $$ \begin{aligned} x &> \frac{-53.55}{21.42} \ x &> -2.5 \end{aligned} $$ ## Convert to interval notation Using the **Interval Notation** knowledge point $$ x \in (-2.5, \infty) $$

(A) $x > 2.5$

(B) $(-2.5, \infty)$

(C) $(-\infty, 2.5)$

(D) $x < -2.5$

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

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QUESTION IMAGE

Question

Explanation:

Expand both sides of the inequality

Simplify the right side

Isolate the variable terms

Solve for x

Convert to interval notation

Answer: