Question

Use set notation to express the value(s) that make the equation 2x=20 true. Enter your response using set notation.(1 point)
Answer
Both −6 and 6 make the equation x^2/2=18 true. Use set notation to express these solutions. When entering your response, list elements in the set from least to greatest, with a comma between each element in the set.(1 point)
Answer
The solution to the inequality 4y+1>17 is y>4. Use set notation to express the values of y that make the inequality 4y+1>17 true.(1 point)
Answer
try again please
Answer
Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8. Sophie says that −2 is a solution. Adola says that 5 is a solution. Gilly says that 2 is a solution. Which person is correct? Enter 1 for Sophie, 2 for Adola, or 3 for Gilly.(1 point)
Answer
Which option correctly describes the values that make the inequality 2m<14 true when written in set notation?

Option #1: {m:m<7}

Option #2: {7:7<m}

Option #3: {m<7:m}

Option #4: {m<7}

(1 point)
Option # correctly states the values that make the inequality true in set notation.
Answered by GPT-4o mini
To solve the equation \(2x = 20\), we first divide both sides by 2:

\[
x = \frac{20}{2} = 10
\]

The solution to the equation is \(x = 10\).

In set notation, we express this solution as:

\[
\{10\}
\]
Answered by GPT-4o mini
To solve the equation \(\frac{x^2}{2} = 18\), we first multiply both sides by 2:

\[
x^2 = 36
\]

Next, we take the square root of both sides:

\[
x = 6 \quad \text{or} \quad x = -6
\]

The solutions to the equation are \(6\) and \(-6\).

In set notation, listing the elements in order from least to greatest, we express this as:

\[
\{-6, 6\}
\]
Answered by GPT-4o mini
To express the solution to the inequality \(4y + 1 > 17\) in set notation, we first solve for \(y\):

1. Subtract 1 from both sides:
\[
4y > 16
\]

2. Divide both sides by 4:
\[
y > 4
\]

The solution to the inequality is \(y > 4\).

In set notation, this is expressed as:

\[
(4, \infty)
\]

This interval notation indicates that \(y\) can take any value greater than 4.
Answered by GPT-4o mini
I apologize for any confusion in my previous response. In set notation, the values of \(y\) that satisfy the inequality \(4y + 1 > 17\), which simplifies to \(y > 4\), can be expressed as follows:

\[
\{ y \in \mathbb{R} \mid y > 4 \}
\]

This notation means "the set of all real numbers \(y\) such that \(y\) is greater than 4."

If you prefer interval notation (which is also a standard way to represent ranges), the solution is:

\[
(4, \infty)
\]

However, since you requested set notation specifically, the first representation is the correct answer. Thank you for your understanding!
Answered by GPT-4o mini
To determine which person is correct, we first need to solve the compound inequality \(-2 \leq 2x - 2 < 8\).

We'll break it down into two parts:

1. **Solving the left part**: \(-2 \leq 2x - 2\)

Add 2 to both sides:
\[
0 \leq 2x
\]
Divide by 2:
\[
0 \leq x \quad \text{or} \quad x \geq 0
\]

2. **Solving the right part**: \(2x - 2 < 8\)

Add 2 to both sides:
\[
2x < 10
\]
Divide by 2:
\[
x < 5
\]

Combining both parts, we have:
\[
0 \leq x < 5
\]

Now we evaluate who among Sophie, Adola, and Gilly is correct:

- **Sophie says \(-2\) is a solution**: This is incorrect because \(-2 < 0\).
- **Adola says \(5\) is a solution**: This is incorrect because \(5\) is not less than \(5\) (not included).
- **Gilly says \(2\) is a solution**: This is correct because \(0 \leq 2 < 5\).

Thus, Gilly is correct. The correct answer is:

**3**
Answered by GPT-4o mini
To solve the inequality \(2m < 14\), we first divide both sides by 2:

\[
m < 7
\]

Now, let's evaluate the provided options for correct set notation that describes the values of \(m\) making the inequality true:

- **Option #1**: \(\{m: m < 7\}\) - This option correctly indicates that \(m\) is any value less than 7. This is the correct set notation.

- **Option #2**: \(\{7: 7 < m\}\) - This option incorrectly suggests that the set contains \(7\) as an element, which is not correct since \(m\) should be less than \(7\).

- **Option #3**: \(\{m < 7: m\}\) - This option is incorrect and does not represent valid set notation.

- **Option #4**: \(\{m < 7\}\) - This option also does not represent values in correct set notation since it does not involve a relationship or a proper statement for \(m\).

Based on this analysis, **Option #1: \(\{m: m < 7\}\)** is the correct choice.