q. solve the inequality.

\-7(x + 3) \ge 4x + 12\

a. $x \le -1$
b. $x \ge -1$
c. $x \le -3$
d. $x \ge -3$

Question

q. solve the inequality.

\-7(x + 3) \ge 4x + 12\

a. $x \le -1$
b. $x \ge -1$
c. $x \le -3$
d. $x \ge -3$

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": [ "Distributive Property", "Solving Linear Inequalities" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Solving Linear Inequalities" ] } ## Expand the left side Using the *Distributive Property* knowledge point $$ -7(x + 3) = -7x - 21 $$ The inequality becomes: $$ -7x - 21 \ge 4x + 12 $$ ## Collect variable terms Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} -7x - 21 - 4x &\ge 12 \ -11x - 21 &\ge 12 \end{aligned} $$ ## Isolate the variable term Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} -11x &\ge 12 + 21 \ -11x &\ge 33 \end{aligned} $$ ## Solve for x Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} x &\le \frac{33}{-11} \ x &\le -3 \end{aligned} $$

A. $x \le -1$

B. $x \ge -1$

C. $x \le -3$

D. $x \ge -3$

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

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QUESTION IMAGE

Question

Explanation:

Expand the left side

Collect variable terms

Isolate the variable term

Solve for x

Answer: