what value of $x$ is in the solution set of the inequality $-5x - 15 10 + 20x$?

-1
1
-2
0

Question

what value of $x$ is in the solution set of the inequality $-5x - 15 > 10 + 20x$?

-1
1
-2
0

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": [ "Solution Set Verification" ], "current_concepts": [ "Solving Linear Inequalities", "Inequality Properties", "Solution Set Verification" ] } ## Isolate the variable terms Using the *Solving Linear Inequalities* knowledge point $$ \begin{aligned} -5x - 15 &> 10 + 20x \ -15 &> 10 + 25x \ -25 &> 25x \end{aligned} $$ ## Solve for x Using the *Inequality Properties* knowledge point $$ \begin{aligned} \frac{-25}{25} &> x \ -1 &> x \ x &< -1 \end{aligned} $$ ## Identify the correct value from the options To find which value of $x$ is in the solution set $x < -1$, we test the given choices: - For $x = -1$: $-1 < -1$ is false. - For $x = 1$: $1 < -1$ is false. - For $x = -2$: $-2 < -1$ is true. - For $x = 0$: $0 < -1$ is false. Thus, only $-2$ satisfies the inequality.

(A) $-1$

(B) $1$

(C) $-2$

(D) $0$

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QUESTION IMAGE

Question

Explanation:

Isolate the variable terms

Solve for x

Identify the correct value from the options

Answer: