Question

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

Answer 1

Its not 4

Answer 2

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

If there's any specific misunderstanding or detail that you would like to clarify, please let me know!