Solve the following inequality and give the solution in interval notation. $$ 5 s-32 $$ or $$ 2 s-1 \leq 7 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. The solution set is the empty set.

Question

Solve the following inequality and give the solution in interval notation. $$ 5 s-3>2 $$ or $$ 2 s-1 \leq 7 $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. The solution set is the empty set.

UpStudy AI · Accepted Answer

To solve the inequality $$ 5s - 3 > 2 $$ **or** $$ 2s - 1 \leq 7 $$, we'll address each part separately and then combine the solutions.

### Step 1: Solve $$ 5s - 3 > 2 $$
1. **Add 3 to both sides:**
   $$
   5s > 5
   $$
2. **Divide by 5:**
   $$
   s > 1
   $$

### Step 2: Solve $$ 2s - 1 \leq 7 $$
1. **Add 1 to both sides:**
   $$
   2s \leq 8
   $$
2. **Divide by 2:**
   $$
   s \leq 4
   $$

### Step 3: Combine the Solutions Using OR
- The solutions are:
  - $$ s > 1 $$
  - **OR** $$ s \leq 4 $$

- **Interpretation:**
  - $$ s > 1 $$ includes all numbers greater than 1.
  - $$ s \leq 4 $$ includes all numbers up to and including 4.
  
- **Union of Solutions:**
  - Any real number satisfies at least one of these conditions.
  - Therefore, the combined solution covers **all real numbers**.

### Final Answer in Interval Notation
The solution set in interval notation is:
$$
(-\infty, \infty)
$$

**Answer Choice:**

**A. The solution set in interval notation is $$ (-\infty, \infty) $$.**
The solution set in interval notation is $$ (-\infty, \infty) $$.

Solve the following inequality and give the solution in interval notation. \( 5 s-3>2 \) or \( 2 s-1 \leq 7 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. The solution set is the empty set.

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