To solve the compound inequality 5x - 4 > 2x + 11, we need to isolate the variable x. Here's how we can do it step by step:
1. Start by subtracting 2x from both sides of the inequality to get rid of the x term on the right side:
5x - 2x - 4 > 2x - 2x + 11.
2. Simplify the equation:
3x - 4 > 11.
3. Next, add 4 to both sides of the inequality to isolate the x term on the left side:
3x - 4 + 4 > 11 + 4.
4. Simplify the equation:
3x > 15.
5. To solve for x, divide both sides of the inequality by 3:
(3x) / 3 > 15 / 3.
6. Simplify the equation:
x > 5.
Therefore, the solution to the compound inequality 5x - 4 > 2x + 11 is x > 5. This means that any value of x greater than 5 will satisfy the inequality.