Question

What is the solution set of: 5x - 5 = 10 and 5x + 4 > 14

Answer 1

To find the solution set for the given equations and inequality, we need to solve each one separately.

### Step 1: Solve the equation \(5x - 5 = 10\)

1. Add 5 to both sides:
\[
5x - 5 + 5 = 10 + 5
\]
\[
5x = 15
\]

2. Divide both sides by 5:
\[
x = \frac{15}{5} = 3
\]

### Step 2: Solve the inequality \(5x + 4 > 14\)

1. Subtract 4 from both sides:
\[
5x + 4 - 4 > 14 - 4
\]
\[
5x > 10
\]

2. Divide both sides by 5:
\[
x > \frac{10}{5} = 2
\]

### Solution Set:

From the first part (the equation), we have:
- \( x = 3 \)

From the second part (the inequality), we have:
- \( x > 2 \)

### Final Solution Set:

Since \(x = 3\) satisfies the inequality \(x > 2\), the solution set is:
- \(x = 3\) or more generally, the solution set can be written as:

\[
\{ x \mid x \geq 3 \}
\]

Thus, the values of \(x\) that satisfy both conditions is \(x \in [3, \infty)\).