what value of $x$ is in the solution set of the inequality $9(2x + 1)

Question

what value of $x$ is in the solution set of the inequality $9(2x + 1) < 9x - 18$?

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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": [ "Distributive Property", "Solving Linear Inequalities", "Inequality Properties" ], "new_concepts": [], "current_concepts": [ "Distributive Property", "Solving Linear Inequalities", "Inequality Properties" ] } ## Expand the left side Using the *Distributive Property* knowledge point $$ 9(2x + 1) = 18x + 9 $$ ## Rewrite the inequality Using the *Solving Linear Inequalities* knowledge point $$ 18x + 9 < 9x - 18 $$ ## Isolate the variable term Using the *Inequality Properties* knowledge point $$ \begin{aligned} 18x - 9x &< -18 - 9 \ 9x &< -27 \end{aligned} $$ ## Solve for x Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} x &< \frac{-27}{9} \ x &< -3 \end{aligned} $$ ## Identify the correct option Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} &\text{We need } x < -3.\ &-4 < -3 \quad (\text{True})\ &-3 < -3 \quad (\text{False})\ &-2 < -3 \quad (\text{False})\ &-1 < -3 \quad (\text{False}) \end{aligned} $$

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QUESTION IMAGE

Question

Explanation:

Expand the left side

Rewrite the inequality

Isolate the variable term

Solve for x

Identify the correct option

Answer: