Question

solve the compound inequality. graph the solution set.

(4(x - 1) < 4) or (2(x + 2) > 4)

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 ______.
(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

$$ 4(x - 1) < 4 $$

$$ x - 1 < 1 $$

$$ x < 2 $$

Step 2: Solve the second inequality

$$ 2(x + 2) > 4 $$

$$ x + 2 > 2 $$

$$ x > 0 $$

Step 3: Combine the solutions using "or"

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

$$ x < 2 \quad \text{or} \quad x > 0 $$

Since every real number is either less than \(2\) or greater than \(0\), the union of these two intervals covers all real numbers:

$$ (-\infty, 2) \cup (0, \infty) = (-\infty, \infty) $$

Answer:

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