1. solve $-4t - 5 2t + 13$ for $t$. $t -3$ $t -9$

Question

1. solve $-4t - 5 > 2t + 13$ for $t$. $t < -9$ $t > -3$ $t < -3$ $t > -9$

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": [ "Linear Equation Solving", "Algebraic Simplification" ], "new_concepts": [ "Solving Linear Inequalities", "Inequality Sign Reversal" ], "current_concepts": [ "Linear Equation Solving", "Algebraic Simplification", "Solving Linear Inequalities", "Inequality Sign Reversal" ] } ## Isolate variable terms Using the **Linear Equation Solving** and **Algebraic Simplification** knowledge points $$ \begin{aligned} -4t - 5 &> 2t + 13 \ -4t - 2t - 5 &> 13 \ -6t - 5 &> 13 \end{aligned} $$ ## Isolate constant terms Using the **Linear Equation Solving** and **Algebraic Simplification** knowledge points $$ \begin{aligned} -6t &> 13 + 5 \ -6t &> 18 \end{aligned} $$ ## Solve for t and reverse inequality sign To solve for $t$, we divide both sides by $-6$. Since we are dividing by a negative number, we must reverse the inequality sign from $>$ to $<$. $$ \begin{aligned} t &< \frac{18}{-6} \ t &< -3 \end{aligned} $$

(A) $t < -9$

(B) $t > -3$

(C) $t < -3$

(D) $t > -9$

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Question

Explanation:

Isolate variable terms

Isolate constant terms

Solve for t and reverse inequality sign

Answer: