What is the solution set of x+2≥6 and 3x≥6 ?(1 point)

Question

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Answer 1

To solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we will solve each one separately:

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

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

Now we have two inequalities:

• \( x \geq 4 \)
• \( x \geq 2 \)

The solution set is determined by the most restrictive inequality, which is \( x \geq 4 \).

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

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

So, to summarize: \[ { x \mid x \geq 4 } \]