what value of $x$ is in the solution set of the inequality $2(3x - 1) \ge 4x - 6$?

-1
-10
-3
-5

Question

what value of $x$ is in the solution set of the inequality $2(3x - 1) \ge 4x - 6$?

-1
-10
-3
-5

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", "Distributive Property", "Inequality Properties", "Solution Set Verification" ], "new_concepts": [], "current_concepts": [ "Solving Linear Inequalities", "Distributive Property", "Inequality Properties", "Solution Set Verification" ] } ## Expand the left side Using the *Distributive Property* knowledge point $$ 2(3x - 1) = 6x - 2 $$ ## Rewrite the inequality Using the *Solving Linear Inequalities* knowledge point $$ 6x - 2 \ge 4x - 6 $$ ## Isolate the variable terms Using the *Inequality Properties* knowledge point $$ \begin{aligned} 6x - 4x &\ge -6 + 2 \ 2x &\ge -4 \end{aligned} $$ ## Solve for x Using the *Inequality Properties* knowledge point $$ \begin{aligned} x &\ge \frac{-4}{2} \ x &\ge -2 \end{aligned} $$ ## Verify the options Using the *Solution Set Verification* knowledge point $$ \begin{aligned} &-1 \ge -2 \quad (\text{True}) \ &-10 \ge -2 \quad (\text{False}) \ &-3 \ge -2 \quad (\text{False}) \ &-5 \ge -2 \quad (\text{False}) \end{aligned} $$

(A) $-1$

(B) $-10$

(C) $-3$

(D) $-5$

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QUESTION IMAGE

Question

Explanation:

Expand the left side

Rewrite the inequality

Isolate the variable terms

Solve for x

Verify the options

Answer: