Question

quiz instructions

for this quiz, answer each question and select the best option from

you have 20 minutes to complete the quiz.

you have only one attempt.

question 1

solve the inequality and give your answer in interval notation.

\\3 \le -2x - 1 \le 11\\

\\(o\\ -2, -6\\)
\\(o\\ (-2, -6)\\)
\\(o\\ -6, -2\\)
\\(o\\ (-6, -2)\\)

Explanation:

⚡ Using what you learned: Solving Compound Inequalities

Step 1: Isolate the variable term

Add \( 1 \) to all parts of the inequality:

$$ 3 + 1 \le -2x - 1 + 1 \le 11 + 1 $$

$$ 4 \le -2x \le 12 $$

Step 2: Divide by the coefficient of \( x \)

Divide all parts by \( -2 \) and reverse the inequality signs because of division by a negative number:

$$ \frac{4}{-2} \ge \frac{-2x}{-2} \ge \frac{12}{-2} $$

$$ -2 \ge x \ge -6 $$

Step 3: Rewrite in standard order and interval notation

Rewrite the inequality from smallest to largest:

$$ -6 \le x \le -2 $$

In interval notation, since both endpoints are included (indicated by \( \le \)), use square brackets:

$$ [-6, -2] $$

Answer:

\( [-6, -2] \) (the third option)