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

Answer 1

To find the solution set for the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we will solve each inequality separately.

1. Solve \( x + 2 \geq 6 \): \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 4 \]

2. Solve \( 3x \geq 6 \): \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq 2 \]

Now, we find the intersection of the two solution sets:

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

The more restrictive condition is \( x \geq 4 \).

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

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

Answer 2

Its not 4

Answer 3

Let's carefully review the inequalities again.

1. Solve \( x + 2 \geq 6 \): \[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 4 \]

2. Solve \( 3x \geq 6 \): \[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq 2 \]

The solutions to the inequalities are:

• From the first inequality: \( x \geq 4 \)
• From the second inequality: \( x \geq 2 \)

Since we are looking for the combined solution of both inequalities, we take the most restrictive condition, which is \( x \geq 4 \).

Therefore, the correct solution set is indeed: \[ { x | x \geq 4 } \]

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