Which set notation correctly expresses the solution set to the equation 31−9x=4 ?(1 point)

Question

Which set notation correctly expresses the solution set to the equation 31−9x=4 ?(1 point)

Responses:
{x=3}
{3}
(x=3)
(3)

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9 answers
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Answer 1

Bot GPT 4-o mini answered
1 month ago

To solve the equation \( 31 - 9x = 4 \):

1. Subtract 31 from both sides:
\[
-9x = 4 - 31
\]
\[
-9x = -27
\]

2. Divide both sides by -9:
\[
x = \frac{-27}{-9}
\]
\[
x = 3
\]

The solution set to the equation is just the value of \( x \), which is 3.

Among the provided choices, the correct notation that expresses the solution set is:
**{3}**

This indicates that the solution set contains the single element 3.

Answer 2

Yes. answered
1 month ago

rey, Amelia, and Cho are discussing the solution set to the equation x2+9=45 .

Trey says the solution is {6} .
Amelia says the solution is {−6,6} .
Cho says the solution is {−6} .
Which person has found the correct solution set?
Responses:
None of them are correct.
Trey
Cho
Amelia

Answer 3

Bot GPT 4-o mini answered
1 month ago

To find the solution set for the equation \( x^2 + 9 = 45 \), we first solve for \( x \):

1. Subtract 9 from both sides:
\[
x^2 = 45 - 9
\]
\[
x^2 = 36
\]

2. Take the square root of both sides:
\[
x = \pm \sqrt{36}
\]
\[
x = \pm 6
\]

So, the solutions are \( x = 6 \) and \( x = -6 \). This means the correct solution set is \( \{-6, 6\} \).

Amelia says the solution is {−6, 6}, which is correct.

Thus, the answer is:
**Amelia**.

Answer 4

Yes. answered
1 month ago

The values −1 and 1 make the equation 3x2+7=10 true. Use set notation to express the solution to the equation.(1 point)

Responses:
(−1,1)
{x=−1,x=1}
{−1,1}
(x=−1,x=1)

Answer 5

Bot GPT 4-o mini answered
1 month ago

The correct solution set to the equation, which contains the values \(-1\) and \(1\), can be expressed in set notation.

Among the options provided, the correct notation for the solution set is:
**\{−1, 1\}**

This notation indicates that the solution set contains the elements \(-1\) and \(1\).

Answer 6

Yes. answered
1 month ago

The solution set of the inequality 3(b−4)+2b>3 is the set of values of b greater than three. Which set notation correctly expresses the solutions?(1 point)

Responses:
{b:b>15}
{b:b<3}
{b:b>3}
{b:b<15}

Answer 7

Bot GPT 4-o mini answered
1 month ago

To solve the inequality \( 3(b - 4) + 2b > 3 \), we can simplify it step by step:

1. Distribute the 3:
\[
3b - 12 + 2b > 3
\]

2. Combine like terms:
\[
5b - 12 > 3
\]

3. Add 12 to both sides:
\[
5b > 15
\]

4. Divide by 5:
\[
b > 3
\]

The solution set is the set of values of \( b \) that are greater than 3.

The correct set notation that expresses these solutions is:
**{b : b > 3}**

Thus, the correct response is:
**{b : b > 3}**.

Answer 8

Yes. answered
1 month ago

What value falls in the solution set of the inequality −3(4k+1)<15

Responses:
−1
−3/2
−5
−4

Answer 9

Bot GPT 4-o mini answered
1 month ago

To solve the inequality \( -3(4k + 1) < 15 \), let's solve it step by step:

1. Distribute the -3:
\[
-12k - 3 < 15
\]

2. Add 3 to both sides:
\[
-12k < 15 + 3
\]
\[
-12k < 18
\]

3. Divide both sides by -12 (remember to flip the inequality when dividing by a negative number):
\[
k > \frac{18}{-12}
\]
\[
k > -\frac{3}{2}
\]

Thus, the solution to the inequality is \( k > -\frac{3}{2} \).

Now, we need to find which of the provided values falls in the solution set \( k > -\frac{3}{2} \):

- **−1**: This is greater than \(-\frac{3}{2}\) (approximately \(-1.5\)), so it satisfies the inequality.
- **−3/2**: This is equal to \(-\frac{3}{2}\), thus does not satisfy \( k > -\frac{3}{2} \).
- **−5**: This is less than \(-\frac{3}{2}\), so it does not satisfy the inequality.
- **−4**: This is also less than \(-\frac{3}{2}\) and does not satisfy the inequality.

Therefore, the value that falls in the solution set of the inequality \( -3(4k + 1) < 15 \) is:
**−1**.