Question

solve the inequality. graph the solution set.

\\3x + 2 < -16 \quad \text{or} \quad 3x - 5 > 10\\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the solution set is \\(\square\\).
(simplify your answer. type your answer in interval notation.)

b. the solution is the empty set.

choose the correct graph below.

a. a number line from -11 to 3 with a left parenthesis at -6 and a bold line extending to the right.
c. a number line from -11 to 3 with a right parenthesis at -6 and a bold line extending to the left.

Explanation:

⚡ Using what you learned: Solving Compound Inequalities

Step 1: Solve the first inequality

$$
LATEXBLOCK0
$$

Step 2: Solve the second inequality

$$
LATEXBLOCK1
$$

Step 3: Combine the solutions

Since the compound inequality uses "or", we take the union of both individual solution sets:

$$ x < -6 \quad \text{or} \quad x > 5 $$

In interval notation, this is written as:

$$ (-\infty, -6) \cup (5, \infty) $$

Step 4: Identify the correct graph

The solution set consists of:

• All numbers strictly less than \(-6\) (represented by a parenthesis pointing left at \(-6\) with shading to the left).
• All numbers strictly greater than \(5\) (represented by a parenthesis pointing right at \(5\) with shading to the right).

Looking at the options:

• Graph C shows a parenthesis at \(-6\) pointing left, with shading extending to the left toward \(-\infty\). This correctly represents the first part of our union, \(x < -6\).

Answer:

Solution Set:
A. The solution set is \((-\infty, -6) \cup (5, \infty)\).

Correct Graph:
C