To find the solution set for the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), let’s solve each one step by step.

Question

1. **Solving the first inequality**:
\[
x + 2 \geq 6
\]
We can get \( x \) alone by subtracting 2 from both sides. So we do:
\[
x \geq 4
\]

2. **Solving the second inequality**:
\[
3x \geq 6
\]
To find \( x \), we divide both sides by 3. That gives us:
\[
x \geq 2
\]

3. **Finding the solution set**:
Now we need to combine what we found. From the first inequality, we got \( x \geq 4 \). From the second one, we found \( x \geq 2 \).

But we have to find the values of \( x \) that work for both inequalities. The first one, \( x \geq 4 \), is the tougher requirement because it’s higher than \( x \geq 2 \).

So, the values that satisfy both inequalities are only those where \( x \) is 4 or more.

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

In simpler terms, this means that \( x \) can be any number that is 4 or greater.

In interval notation, we can write this as:
\[
[4, \infty)
\]make this smaller

Answer 1

To find the solution set for the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we solve each one step by step.

1. Solving the first inequality: \[ x + 2 \geq 6 \] Subtracting 2 from both sides gives: \[ x \geq 4 \]

2. Solving the second inequality: \[ 3x \geq 6 \] Dividing both sides by 3 results in: \[ x \geq 2 \]

3. Finding the solution set: We need the values of \( x \) that satisfy both inequalities: \( x \geq 4 \) and \( x \geq 2 \). The more restrictive condition is \( x \geq 4 \).

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

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