Question

What is a solution set of 2x-3=5 and 5x+3 > -12?

Answer 1

To find the solution set of the equations \(2x - 3 = 5\) and the inequality \(5x + 3 > -12\), we will solve each one separately and then find the intersection of their solutions.

1. **Solve the equation \(2x - 3 = 5\)**:

\[
2x - 3 = 5
\]
Add 3 to both sides:
\[
2x = 5 + 3
\]
\[
2x = 8
\]
Divide by 2:
\[
x = 4
\]

2. **Solve the inequality \(5x + 3 > -12\)**:

\[
5x + 3 > -12
\]
Subtract 3 from both sides:
\[
5x > -12 - 3
\]
\[
5x > -15
\]
Divide by 5 (and since 5 is a positive number, the inequality remains the same):
\[
x > -3
\]

3. **Combine the solutions**:

The solution to the equation \(2x - 3 = 5\) gives us \(x = 4\).
The solution to the inequality \(5x + 3 > -12\) gives us \(x > -3\).

Since \(x = 4\) satisfies \(x > -3\), the combined solution set is simply \(x = 4\).

**Final Answer**: The solution set is \(\{4\}\).