Question

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

Answer 1

What is the solution set of 2x−3=5 and 5x+3>−12 ?(1 point) put it in a way that is less complicated

Answer 2

Use the image to answer the question.

A number line ranges from negative 5 to 5 in increments of 1. An open point is plotted at 2, with a solid line extending right, beyond 5. An open point is plotted at 0, with a dotted line extending left, beyond negative 5.

What is the solution set to the inequalities on the graph?

(1 point)
x<
or x>

Answer 3

Use the image to answer the question.

A number line extends from negative 5 to 5 in increments of 1.

To indicate the solution for x≥−1 and x<4 , where would you place circles on the graph? Enter the lesser value first.

(1 point)
and

Answer 4

Use the image to answer the question.

A number line ranges from negative 3 to 8 in increments of 1. Two closed points are plotted at negative 2 and 7, with a solid line extending between them.

What solution set does the graph represent?

(1 point)
x≤
and x≥

Answer 5

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

The solution set that satisfies both inequalities is the intersection of \( x \geq 4 \) and \( x \geq 2 \). Since \( x \geq 4 \) is the more restrictive condition, the final solution set is:

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

In interval notation, this can be expressed as:
\[
[4, \infty)
\]

Answer 6

Let's solve the equations and inequalities step by step to find the solution set.

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

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

Now we have:
- From the equation: \( x = 4 \)
- From the inequality: \( x > -3 \)

**Conclusion**: The solution set that meets both conditions is just the single point where the equation is satisfied, which is \( x = 4 \).

Thus, the final answer can be expressed as:
\[
\{ x \mid x = 4 \}
\]

Or simply:
\[
\{ 4 \}
\]

Answer 7

Based on your description of the number line:

1. There is an **open point** at 2, with a **solid line extending right** beyond 5. This indicates that the inequality is:
\[
x > 2
\]

2. There is an **open point** at 0, with a **dotted line extending left** beyond -5. This indicates that the inequality is:
\[
x < 0
\]

Therefore, the solution set for the inequalities represented on the graph is:
\[
x < 0 \quad \text{or} \quad x > 2
\]

In interval notation, this can be expressed as:
\[
(-\infty, 0) \cup (2, \infty)
\]

So, the final response to your question is:
\[
x < 0 \quad \text{or} \quad x > 2
\]

Answer 8

Based on the inequalities \( x \geq -1 \) and \( x < 4 \):

1. **For \( x \geq -1 \)**: You would place a solid circle (or closed circle) on -1 to indicate that -1 is included in the solution set.

2. **For \( x < 4 \)**: You would place an open circle on 4 to indicate that 4 is not included in the solution set.

So, you would place the circles as follows:
- **Solid circle at** \(-1\)
- **Open circle at** \(4\)

In terms of just placing the numbers:
- \(-1\) (with a solid circle)
- \(4\) (with an open circle)

Thus, entering the lesser value first, you would write:
\[
-1 \text{ and } 4
\]

Answer 9

Based on your description of the number line:

1. **Closed points at -2 and 7** indicate that both -2 and 7 are included in the solution set.

2. **A solid line extending between -2 and 7** indicates all the values between -2 and 7 are included.

This corresponds to the following inequalities:

- Since there is a closed point at -2, we have \( x \geq -2 \).
- Since there is a closed point at 7, we have \( x \leq 7 \).

Thus, the solution set represented by the graph is:
\[
x \geq -2 \quad \text{and} \quad x \leq 7
\]

In summary, the answer is:
- \( x \geq -2 \)
- \( x \leq 7 \)

You can express the interval notation for this solution set as:
\[
[-2, 7]
\]