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 \(x \in [3, \infty)\).