Question

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

Answer 1

incorrect give me a different answer

Answer 2

i didn't say clarify, I said give me a different answer, because that ones wrong

Answer 3

what part of give me a different answer can you not comprehend? give me a different answer that isn't 4

Answer 4

What is the solution set of 2x−3=5
and 5x+3>−12

Answer 5

To solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \), we'll solve each inequality separately.

1. **For \( x + 2 \geq 6 \)**:
\[
x + 2 - 2 \geq 6 - 2
\]
\[
x \geq 4
\]

2. **For \( 3x \geq 6 \)**:
\[
\frac{3x}{3} \geq \frac{6}{3}
\]
\[
x \geq 2
\]

Now, we have the two inequalities:
- \( x \geq 4 \)
- \( x \geq 2 \)

The solution set is determined by the more restrictive condition, which is \( x \geq 4 \). Therefore, the combined solution set for both inequalities is:

\[
\{ x \mid x \geq 4 \}
\]

So the final answer is:
\[
\{ x \mid x \geq 4 \}
\]

Answer 6

Let's carefully re-evaluate the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \).

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

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

Now, we have:
- From the first inequality, \( x \geq 4 \)
- From the second inequality, \( x \geq 2 \)

To find the solution set for both inequalities, we must consider the restriction imposed by \( x \geq 4 \) (since it is more restrictive).

Thus, the intersection of these two solution sets is:
\[
x \geq 4
\]

The solution set is:
\[
\{ x \mid x \geq 4 \}
\]

If you meant the solution to the combined inequalities using "and" or any additional constraints, the response remains valid. If you had something different in mind, please clarify so I can assist you accurately!

Answer 7

I apologize for any confusion. Let's double-check the inequalities to ensure we derive the correct solution together.

We start with the following inequalities:

1. \( x + 2 \geq 6 \)
2. \( 3x \geq 6 \)

Let's solve each inequality step by step:

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

### Inequality 2: \( 3x \geq 6 \)
Divide both sides by 3:
\[
x \geq 2
\]

### Combined Conditions
Now we have:
- From the first inequality: \( x \geq 4 \)
- From the second inequality: \( x \geq 2 \)

Since we want the values of \( x \) that satisfy both inequalities simultaneously (the conjunction "and"), we take the more restrictive condition, which is \( x \geq 4 \).

Therefore, the final answer is indeed still:
\[
\{ x \mid x \geq 4 \}
\]

If your expectation is different regarding the solution or context, please let me know, and I will do my best to provide the answer you need.

Answer 8

I apologize for misunderstanding your request. Since the inequalities you provided have been solved correctly as \( x \geq 4 \) and \( x \geq 2 \), the intersection indeed leads us to \( x \geq 4 \).

However, if you're asking for a different interpretation or perhaps a different way to express the solution:

For the two inequalities:
1. \( x + 2 \geq 6 \) leads to \( x \geq 4 \)
2. \( 3x \geq 6 \) leads to \( x \geq 2 \)

The entire solution set can also be expressed differently, such as:
- In interval notation, you can say the solution is \( [4, \infty) \).

Alternatively, if you were looking for a specific example of a value satisfying the conditions of both inequalities, you could say any number greater than or equal to 4, such as \( x = 5 \) or \( x = 10 \).

In a broader sense, you could formulate it as:
- Any \( x \) where \( x \in \{2, 3\} \) does not satisfy both conditions but \( x \in \{4, 5, 6,\ldots\} \) would work.

Again, I appreciate your patience, and if you have a more specific direction in mind for a "different answer," please let me know!

Answer 9

Let's solve the equations and inequalities step by step.

### 1. Solve the equation \( 2x - 3 = 5 \):
Add 3 to both sides:
\[
2x - 3 + 3 = 5 + 3
\]
\[
2x = 8
\]
Now divide both sides by 2:
\[
x = 4
\]

### 2. Solve the inequality \( 5x + 3 > -12 \):
Subtract 3 from both sides:
\[
5x + 3 - 3 > -12 - 3
\]
\[
5x > -15
\]
Now divide both sides by 5:
\[
x > -3
\]

### Now, combine the results:
The solution to the equation gives us \( x = 4 \).

The solution to the inequality tells us that \( x \) can be any value greater than \(-3\).

### Finding the common solution:
We need the value of \( x \) that satisfies **both** statements. The equation \( x = 4 \) satisfies the inequality \( x > -3 \) because \( 4 > -3 \).

### Conclusion:
Thus, the solution set that satisfies both \( 2x - 3 = 5 \) and \( 5x + 3 > -12 \) can be expressed as:
\[
\{ x \mid x = 4 \}
\]

If you want the solution explicitly denoting it:
- The solution set is simply \( \{4\} \).