2.6 compound inequalities quiz

solve for x:

(-7x - 50 \le -1\\) and (-6x + 70 > -2\\)

there are infinitely many solutions

(-7 \le x < 12\\)

there are no solutions

(x \ge -7\\) or (x < 12\\)

Question

2.6 compound inequalities quiz

solve for x:

(-7x - 50 \le -1\) and (-6x + 70 > -2\)

there are infinitely many solutions

(-7 \le x < 12\)

there are no solutions

(x \ge -7\) or (x < 12\)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [], "new_concepts": [ "Compound Inequalities", "Intersection of Sets" ], "current_concepts": [ "Compound Inequalities", "Linear Inequalities", "Intersection of Sets" ] } ## Solve the first inequality $$ \begin{aligned} -7x - 50 &\le -1 \ -7x &\le 49 \ x &\ge -7 \end{aligned} $$ ## Solve the second inequality $$ \begin{aligned} -6x + 70 &> -2 \ -6x &> -72 \ x &< 12 \end{aligned} $$ ## Find the intersection of the solution sets $$ \begin{aligned} x \ge -7 \quad &\text{and} \quad x < 12 \ -7 &\le x < 12 \end{aligned} $$

There are infinitely many solutions

$-7 \le x < 12$

There are no solutions

$x \ge -7 \text{ or } x < 12$

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QUESTION IMAGE

Question

Explanation:

Solve the first inequality

Solve the second inequality

Find the intersection of the solution sets

Answer: