What is the solution set of 2x−3=5 and 5x+3>−12 ?(1 point)

To find the solution set for the equations \( 2x - 3 = 5 \) and \( 5x + 3 > -12 \), we will solve each inequality separately.

1. **Solve the equation \( 2x - 3 = 5 \)**:
\[
2x - 3 = 5
\]
Add 3 to both sides:
\[
2x = 8
\]
Divide by 2:
\[
x = 4
\]

2. **Solve the inequality \( 5x + 3 > -12 \)**:
\[
5x + 3 > -12
\]
Subtract 3 from both sides:
\[
5x > -15
\]
Divide by 5:
\[
x > -3
\]

3. **Combine the results**:
The solution to \( 2x - 3 = 5 \) gives us \( x = 4 \), and the solution to \( 5x + 3 > -12 \) gives us \( x > -3 \).

4. **Determine the overall solution set**:
Since \( 4 > -3 \), the solution set for both conditions is \( x \) must be both \( 4 \) (from the equality) and greater than \(-3\) (from the inequality). Since the equality provides a specific value, the solution set is \( x = 4 \).

Thus, the solution set is:
\[
\{ x = 4 \}
\]