The solutions to the equation \( x^2 = 18 \) are \( -6 \) and \( 6 \). In set notation, the solutions can be written as:
\[ { -6, 6 } \]
Both −6
−
6
and 6 make the equation x22=18
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).
11 answers
The solution to the inequality 4y+1>17
4
𝑦
+
1
>
17
is y>4
𝑦
>
4
. Use set notation to express the values of y that make the inequality 4y+1>17
4
𝑦
+
1
>
17
true.(1 point)
{:
:
}
Check answer
4
𝑦
+
1
>
17
is y>4
𝑦
>
4
. Use set notation to express the values of y that make the inequality 4y+1>17
4
𝑦
+
1
>
17
true.(1 point)
{:
:
}
Check answer
The solution to the inequality \( 4y + 1 > 17 \) is indeed \( y > 4 \). In set notation, this can be expressed as:
\[ { y \in \mathbb{R} \mid y > 4 } \]
This notation indicates that \( y \) is a member of the real numbers and must be greater than 4.
Sophie, Adola, and Gilly are debating potential values in the solution set of the compound inequality −2≤2x−2<8
−
2
≤
2
𝑥
−
2
<
8
. Sophie says that −2
−
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)
The person who is correct is person .
−
2
≤
2
𝑥
−
2
<
8
. Sophie says that −2
−
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)
The person who is correct is person .
To solve the compound inequality \(-2 \leq 2x - 2 < 8\), we will break it down into two parts.
-
First part: \[ -2 \leq 2x - 2 \] Add 2 to both sides: \[ 0 \leq 2x \] Divide by 2: \[ 0 \leq x \quad \text{or} \quad x \geq 0 \]
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Second part: \[ 2x - 2 < 8 \] Add 2 to both sides: \[ 2x < 10 \] Divide by 2: \[ x < 5 \]
Combining both parts, the solution to the compound inequality is: \[ 0 \leq x < 5 \] or in interval notation: \[ [0, 5) \]
Now we will check the proposed solutions:
- Sophie says \( -2 \): Not valid, since \(-2 < 0\).
- Adola says \( 5 \): Not valid, since \(5\) is not less than \(5\).
- Gilly says \( 2 \): Valid, since \(2\) is between \(0\) and \(5\).
The correct person is 3 for Gilly.
Which option correctly describes the values that make the inequality 2m<14
2
𝑚
<
14
true when written in set notation?
Option #1: {m:m<7}
{
𝑚
:
𝑚
<
7
}
Option #2: {7:7<m}
{
7
:
7
<
𝑚
}
Option #3: {m<7:m}
{
𝑚
<
7
:
𝑚
}
Option #4: {m<7}
{
𝑚
<
7
}
(1 point)
Option # correctly states the values that make the inequality true in set notation.
2
𝑚
<
14
true when written in set notation?
Option #1: {m:m<7}
{
𝑚
:
𝑚
<
7
}
Option #2: {7:7<m}
{
7
:
7
<
𝑚
}
Option #3: {m<7:m}
{
𝑚
<
7
:
𝑚
}
Option #4: {m<7}
{
𝑚
<
7
}
(1 point)
Option # correctly states the values that make the inequality true in set notation.
To solve the inequality \( 2m < 14 \), we first divide both sides by 2:
\[ m < 7 \]
Now, we need to express this solution in set notation. The correct notation for the values that satisfy this inequality is:
\[ { m : m < 7 } \]
Now, let's analyze the options given:
- Option #1: \({ m : m < 7 }\) - This correctly describes the solution.
- Option #2: \({ 7 : 7 < m }\) - Incorrect, as it indicates values greater than 7.
- Option #3: \({ m < 7 : m }\) - Incorrect format.
- Option #4: \({ m < 7 }\) - Incorrect formatting, as this does not follow the proper set notation.
Therefore, Option #1 correctly states the values that make the inequality true in set notation.
Which set notation correctly expresses the solution set to the equation 31−9x=4 ?(1 point)
Responses
(3)
left parenthesis 3 right parenthesis
(x=3)
left parenthesis x equals 3 right parenthesis
{x=3}
left brace x equals 3 right brace
{3}
Responses
(3)
left parenthesis 3 right parenthesis
(x=3)
left parenthesis x equals 3 right parenthesis
{x=3}
left brace x equals 3 right brace
{3}
To solve the equation \( 31 - 9x = 4 \), let's isolate \( x \).
-
Subtract 31 from both sides: \[ -9x = 4 - 31 \] \[ -9x = -27 \]
-
Divide both sides by -9: \[ x = \frac{-27}{-9} = 3 \]
Thus, the solution to the equation is \( x = 3 \).
Now let's look at the provided response options for how to correctly express this solution in set notation:
- (3) - This is not a valid set notation; it's a single number.
- (x = 3) - This is not set notation; it describes the solution, but is not in set notation form.
- {x = 3} - This is a valid set notation expressing that \( x \) is equal to 3.
- {3} - This is also a valid set notation indicating the solution, specifying the value of \( x \).
Both {x = 3} and {3} are technically valid depending on the context. However, the most common and straightforward set notation for expressing the solution to the equation would be {3}.
Thus, the answer you would want to choose is {3}.
Trey, 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?
(1 point)
Responses
Trey
Trey
Cho
Cho
None of them are correct.
None of them are correct.
Amelia
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?
(1 point)
Responses
Trey
Trey
Cho
Cho
None of them are correct.
None of them are correct.
Amelia
To solve the equation \( x^2 + 9 = 45 \), we first isolate \( x^2 \):
-
Subtract 9 from both sides: \[ x^2 = 45 - 9 \] \[ x^2 = 36 \]
-
Now take the square root of both sides: \[ x = \pm 6 \]
The solutions are \( x = 6 \) and \( x = -6 \).
Now let's review the responses:
- Trey says the solution is {6}. (Incorrect, since both \( 6 \) and \( -6 \) are solutions.)
- Amelia says the solution is {−6, 6}. (Correct, this includes both solutions.)
- Cho says the solution is {−6}. (Incorrect, since both \( 6 \) and \( -6 \) are solutions.)
The correct person is Amelia.