Question

solve the compound inequality. graph the solution set.

\\ -6x + 4x - 1 > 11 \text{ or } 4x > 2x + 8 \\

write the solution using interval notation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is \dots.
(simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression.)

b. the solution is the empty set.

Explanation:

⚡ Using what you learned: Solving Compound Inequalities

Step 1: Solve the first inequality

$$ -6x + 4x - 1 > 11 $$

$$ -2x - 1 > 11 $$

$$ -2x > 12 $$

$$ x < -6 $$

Step 2: Solve the second inequality

$$ 4x > 2x + 8 $$

$$ 2x > 8 $$

$$ x > 4 $$

Step 3: Combine the solutions

The compound inequality uses "or", which represents the union of the two individual solution sets:

$$ x < -6 \quad \text{or} \quad x > 4 $$

In interval notation, this is written as:

$$ (-\infty, -6) \cup (4, \infty) $$

Answer:

A. The solution set is \((-\infty, -6) \cup (4, \infty)\).