what value of $x$ is in the solution set of the inequality $4x - 12 \le 16 + 8x$?

-8
-7
-10
-9

Question

what value of $x$ is in the solution set of the inequality $4x - 12 \le 16 + 8x$?

-8
-7
-10
-9

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Solving Linear Inequalities", "Inequality Properties" ], "new_concepts": [], "current_concepts": [ "Solving Linear Inequalities", "Inequality Properties", "Interval Notation" ] } ## Isolate the variable terms Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} 4x - 12 &\le 16 + 8x \ -12 &\le 16 + 4x \end{aligned} $$ ## Isolate the constant terms Using the *Inequality Properties* knowledge point $$ \begin{aligned} -12 - 16 &\le 4x \ -28 &\le 4x \end{aligned} $$ ## Solve for x Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} \frac{-28}{4} &\le x \ -7 &\le x \quad \text{or} \quad x \ge -7 \end{aligned} $$ ## Identify the correct value from the options Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} &\text{Solution set: } \{x \mid x \ge -7\} \ &\text{Comparing options: } \ &-8 \ge -7 \quad (\text{False}) \ &-7 \ge -7 \quad (\text{True}) \ &-10 \ge -7 \quad (\text{False}) \ &-9 \ge -7 \quad (\text{False}) \end{aligned} $$

(A) $-8$

(B) $-7$

(C) $-10$

(D) $-9$

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QUESTION IMAGE

Question

Explanation:

Isolate the variable terms

Isolate the constant terms

Solve for x

Identify the correct value from the options

Answer: