which graph represents the solution of the inequality below?

(-1.2x - 6.5x \le 2.3x + 5)

Question

which graph represents the solution of the inequality below?

(-1.2x - 6.5x \le 2.3x + 5)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Solving Inequalities", "Inequality Graphing" ], "current_concepts": [ "Linear Inequalities", "Solving Inequalities", "Inequality Graphing" ] } ## Combine like terms on the left side $$ \begin{aligned} -1.2x - 0.5x &\le 2.3x + 5 \ -1.7x &\le 2.3x + 5 \end{aligned} $$ ## Isolate the variable x $$ \begin{aligned} -1.7x - 2.3x &\le 5 \ -4x &\le 5 \end{aligned} $$ ## Divide by -4 and reverse the inequality sign $$ \begin{aligned} x &\ge \frac{5}{-4} \ x &\ge -1.25 \end{aligned} $$ The graph representing $x \ge -1.25$ has a solid circle at $-1.25$ (between $-1$ and $-2$, closer to $-1$) with an arrow pointing to the right. Looking at the options, the third graph has a solid circle at approximately $-1.25$ with an arrow pointing to the right.

(A) Solid circle at -0.5, arrow pointing left

(B) Solid circle at -2, arrow pointing left

(C) Solid circle at -1.25, arrow pointing right

(D) Solid circle at 2, arrow pointing right

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

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QUESTION IMAGE

Question

Explanation:

Combine like terms on the left side

Isolate the variable x

Divide by -4 and reverse the inequality sign

Answer: