Question

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

Answer 1

To solve the problem, we need to find the solution set for both equations: \(2x - 3 = 5\) and \(5x + 3 > -12\).

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**:
- From the first equation, we have \(x = 4\).
- From the inequality, we have \(x > -3\).

Since \(x = 4\) satisfies the inequality \(x > -3\), the solution set includes \(x = 4\).

Thus, the complete solution set can be expressed as:
\[
\{ 4 \}
\]

In conclusion, the solution set for the given equations is \(\{ 4 \}\).