question 1 a)what is the solution set of x+2≥6 and 3x≥6?(1 point) {x|x$$} question 2 a)what is the solution set of 2x−3=5 and 5x+3>−12 ?(1 point) {$$}

Answer 1

Let's solve each question step by step.

Question 1:

We need to solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \).

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

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

Now we need to find the intersection of the two solution sets:

• From \( x + 2 \geq 6 \), we have \( x \geq 4 \).
• From \( 3x \geq 6 \), we have \( x \geq 2 \).

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

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

Question 2:

We need to solve the equation \( 2x - 3 = 5 \) and the inequality \( 5x + 3 > -12 \).

1. Solve \( 2x - 3 = 5 \): \[ 2x - 3 = 5 \ 2x = 5 + 3 \ 2x = 8 \ x = \frac{8}{2} \ x = 4 \]

2. Solve \( 5x + 3 > -12 \): \[ 5x + 3 > -12 \ 5x > -12 - 3 \ 5x > -15 \ x > \frac{-15}{5} \ x > -3 \]

Now, we have:

• The solution from \( 2x - 3 = 5 \) gives \( x = 4 \).
• The solution from \( 5x + 3 > -12 \) gives \( x > -3 \).

Since we are looking for the solution that meets both conditions, we have:

• \( x = 4 \) satisfies \( x > -3 \).

Solution set: \[ {x | x = 4} \]

Final Answers:

1. Question 1: \({x | x \geq 4}\)
2. Question 2: \({x | x = 4}\)

Answer 2

Q1 IS WRONG

Answer 3

Let's carefully reevaluate Question 1 and solve the inequalities step by step again.

Question 1:

We need to solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \).

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

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

Next, we need the combined solution for the inequalities. We have:

• From \( x + 2 \geq 6 \), we have \( x \geq 4 \).
• From \( 3x \geq 6 \), we have \( x \geq 2 \).

Combining the Solutions:

The inequality \( x \geq 4 \) is more restrictive than \( x \geq 2 \). Therefore, the overall solution set is determined by the more stringent inequality.

Final Solution Set: \[ { x | x \geq 4 } \]

Since the solution holds true, if there's something specific that you believe is wrong, please clarify what aspect you find incorrect!

Answer 4

Q1 is = What is the solution set of x + 2 greater than or equal two 6 and 3x is greater than or equal to 6

Answer 5

Thank you for your clarification! Let's solve the inequalities correctly based on your phrasing:

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

We'll solve each inequality separately and then find the solution set that satisfies both.

Step 1: Solve \( x + 2 \geq 6 \)

\[ x + 2 \geq 6 \] Subtract 2 from both sides: \[ x \geq 6 - 2 \] \[ x \geq 4 \]

Step 2: Solve \( 3x \geq 6 \)

\[ 3x \geq 6 \] Divide both sides by 3: \[ x \geq \frac{6}{3} \] \[ x \geq 2 \]

Conclusion: Combine the Solutions

From the two inequalities, we find:

• From \( x + 2 \geq 6 \): \( x \geq 4 \)
• From \( 3x \geq 6 \): \( x \geq 2 \)

The solution set that satisfies both inequalities is determined by the more restrictive condition. In this case, \( x \geq 4 \) is more restrictive than \( x \geq 2 \).

Final Solution Set:

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

If you intended for something different in your question, please let me know!

Answer 6

Its not four give me a diferent answer

Answer 7

Let’s carefully re-evaluate and clarify the solution step by step again, ensuring there are no mistakes.

Given Inequalities:

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

Step 1: Solve \( x + 2 \geq 6 \)

Subtract 2 from both sides: \[ x \geq 6 - 2 \] \[ x \geq 4 \]

Step 2: Solve \( 3x \geq 6 \)

Divide both sides by 3: \[ x \geq \frac{6}{3} \] \[ x \geq 2 \]

Conclusion: Combine the Solutions

The two inequalities yield:

1. From \( x + 2 \geq 6 \): \( x \geq 4 \)
2. From \( 3x \geq 6 \): \( x \geq 2 \)

Now, if we look at the solutions together:

• The first inequality tells us \( x \) must be at least 4.
• The second inequality tells us \( x \) must be at least 2.

The intersection of both inequalities is determined by the more restrictive condition, which is \( x \geq 4 \). Therefore, this means every solution that satisfies both conditions must be at least 4.

Final Solution Set:

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

If there's a misunderstanding or if you are seeking a specific kind of response (such as a different interpretation of the inequalities), please provide further details! I am here to help.

Answer 8

what does geq 4 mean?

Answer 9

The notation \( \geq \) stands for "greater than or equal to." Therefore, when we write \( x \geq 4 \), it means that \( x \) can take any value that is either:

• Greater than 4 (e.g., 5, 6, 7, etc.)
• Equal to 4 (i.e., \( x = 4 \))

In set notation, the solution \( { x | x \geq 4 } \) represents all numbers \( x \) such that \( x \) is greater than or equal to 4. It includes 4 itself and all numbers that follow it on the number line.

If there's something else you'd like to understand or if you have additional questions, feel free to ask!