What is the solution set of x+2≥6x+2≥6 and 3x≥63x≥6 ?(1 point) {x|xx|x}

Answer 1

To solve the inequalities you've provided, let's break them down step by step.

First Inequality: \( x + 2 \geq 6 \)

1. Subtract 2 from both sides: \[ x \geq 4 \]

Second Inequality: \( 3x \geq 6 \)

1. Divide both sides by 3: \[ x \geq 2 \]

Combining the Solutions

Now, we need to combine the solution sets from the two inequalities.

• From the first inequality, the solution set is \( x \geq 4 \).
• From the second inequality, the solution set is \( x \geq 2 \).

The overall solution set must satisfy both inequalities. The more restrictive solution is \( x \geq 4 \).

Final Solution Set

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

This indicates that \( x \) can take any value equal to or greater than 4.

Answer 2

x+2>=6 and 3x>= 6

Answer 3

Let's solve each inequality step by step.

First Inequality: \( x + 2 \geq 6 \)

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

Second Inequality: \( 3x \geq 6 \)

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

Combined Solution

Now we combine the solutions from both inequalities:

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

Since \( x \) must satisfy both conditions, we take the more restrictive condition:

\[ x \geq 4 \]

Final Solution Set

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

This means \( x \) can be any value that is 4 or greater.

Answer 4

What is the solution set of x+2>=6 and 3x>= 6

Answer 5

Let's solve the inequalities step by step:

Inequality 1: \( x + 2 \geq 6 \)

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

Inequality 2: \( 3x \geq 6 \)

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

Combined Solution

Now we need to find the solution set that satisfies both inequalities.

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

The more restrictive condition is \( x \geq 4 \). Therefore, we combine the two inequalities by taking the intersection of the solution sets:

Final Solution Set

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

This means \( x \) can take any value that is 4 or greater.

Answer 6

wrong

Answer 7

I apologize for any confusion in my previous responses. Let’s carefully solve the inequalities \( x + 2 \geq 6 \) and \( 3x \geq 6 \) step by step.

Inequality 1: \( x + 2 \geq 6 \)

To solve for \( x \):

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

Inequality 2: \( 3x \geq 6 \)

To solve for \( x \):

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

Combined Solution

Now we consider both inequalities:

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

To satisfy both inequalities simultaneously, we take the more restrictive condition, which is \( x \geq 4 \).

Conclusion

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

This indicates that \( x \) can take any value that is 4 or greater.

If you meant to combine these inequalities in a different way or there is any other clarification needed, please let me know!