Question

quiz-- section 8.6
started: jun 22 at 6:34pm
quiz instructions
for this quiz, answer each question and select the best option from the
you have 20 minutes to complete the quiz.
you have only one attempt.

question 4
solve the following inequality and give your answers in interval notation
\\6k - 1 > 29 \quad \text{or} \quad 4 - 5k > -1\\

(1, 5)
\\((-\infty, 1) \cup (5, \infty)\\)
\\((5, \infty)\\)
\\((-\infty, 5) \cup (1, \infty)\\)

Explanation:

⚡ Using what you learned: Solving Compound Inequalities

Step 1: Solve the first inequality

$$ 6k - 1 > 29 $$

$$ 6k > 30 $$

$$ k > 5 $$

Step 2: Solve the second inequality

Remember to flip the inequality sign when dividing by a negative number.

$$ 4 - 5k > -1 $$

$$ -5k > -5 $$

$$ k < 1 $$

Step 3: Combine with "or" and write in interval notation

The word "or" represents the union (\(\cup\)) of the two solution sets:

$$ k < 1 \quad \text{or} \quad k > 5 $$

In interval notation, this is written as:

$$ (-\infty, 1) \cup (5, \infty) $$

Answer:

$$ (-\infty, 1) \cup (5, \infty) $$