what is the solution set of x + 2 ≥ 6 and 3x ≥ 6

Question

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Answer 1

To solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we'll solve each inequality separately.

1. Solve \( x + 2 \geq 6 \): \[ x + 2 - 2 \geq 6 - 2 \ x \geq 4 \]

2. Solve \( 3x \geq 6 \): \[ \frac{3x}{3} \geq \frac{6}{3} \ x \geq 2 \]

Next, we combine the solutions from both inequalities. The solution set is determined by the intersection of the two results:

• From the first inequality, we have \( x \geq 4 \).
• From the second inequality, we have \( x \geq 2 \).

Since \( x \geq 4 \) is more restrictive than \( x \geq 2 \), the solution set that satisfies both inequalities is \( x \geq 4 \).

Therefore, the solution set can be expressed as:

\[ {x | x \geq 4} \]