What is the solution set of x+2≥6

Question

and 3x≥6
?(1 point)
{x|x
}

Answer 1

To solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), let's solve each inequality separately:

1. For the first inequality, \( x + 2 \geq 6 \): \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 4 \]

2. For the second inequality, \( 3x \geq 6 \): \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq 2 \]

Now, we need to find the solution set that satisfies both inequalities simultaneously. The first inequality gives \( x \geq 4 \) and the second gives \( x \geq 2 \). The more restrictive condition is \( x \geq 4 \).

Therefore, the solution set is: \[ {x \mid x \geq 4} \]

In interval notation, this is represented as: \[ [4, \infty) \]