What is the solution set of: x + 1 ≥ 5 and 2x ≥ 4

Answer 1

To solve the inequalities \( x + 1 \geq 5 \) and \( 2x \geq 4 \), we will solve each inequality separately and then find the intersection of their solution sets.

1. Solve the first inequality: \[ x + 1 \geq 5 \] Subtract 1 from both sides: \[ x \geq 4 \]

2. Solve the second inequality: \[ 2x \geq 4 \] Divide both sides by 2: \[ x \geq 2 \]

3. Combine the solutions: The solution for the first inequality is \( x \geq 4 \) and for the second is \( x \geq 2 \). The combined solution set must satisfy both conditions, which is determined by the more restrictive inequality.

Thus, the solution set is \( x \geq 4 \).

In interval notation, the solution set is: \[ [4, \infty) \]