To find the solution set for the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we solve each inequality separately.
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Solve the first inequality: \[ x + 2 \geq 6 \] Subtract \( 2 \) from both sides: \[ x \geq 4 \]
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Solve the second inequality: \[ 3x \geq 6 \] Divide both sides by \( 3 \): \[ x \geq 2 \]
Now we have two inequalities:
- \( x \geq 4 \)
- \( x \geq 2 \)
Next, we find the intersection of both solutions. The inequality \( x \geq 4 \) is a stronger restriction compared to \( x \geq 2 \), so the solution to the system of inequalities is: \[ x \geq 4 \]
Thus, the solution set in set notation is: \[ { x | x \geq 4 } \]