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

Question

Responses

(x=−1,x=1)
left parenthesis x equals negative 1 comma x equals 1 right parenthesis

(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

​ {x=−1,x=1}
​ left brace x equals negative 1 comma x equals 1 right brace

{−1,1}
left brace negative 1 comma 1 right brace.

Answer 1

The correct way to express the solution to the equation in set notation is:

\({-1, 1}\)

So the response is:

{−1,1} left brace negative 1 comma 1 right brace.

Answer 2

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}
left brace b colon b less than 15 right brace

{b:b>3}
left brace b colon b greater than 3 right brace

{b:b<3}
left brace b colon b less than 3 right brace

{b:b>15}
left brace b colon b greater than 15 right brace

Answer 3

The correct set notation that expresses the solutions for the inequality \(3(b - 4) + 2b > 3\), resulting in \(b > 3\), is:

\({b : b > 3}\)

So the response is:

{b:b>3} left brace b colon b greater than 3 right brace.

Answer 4

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

−5
negative 5

−32
Start Fraction negative 3 over 2 End Fraction

−1
negative 1

−4

Answer 5

To solve the inequality \(-3(4k + 1) < 15\), we first distribute the \(-3\):

\[ -12k - 3 < 15 \]

Next, we add \(3\) to both sides:

\[ -12k < 18 \]

Now, we divide both sides by \(-12\). Remember that when dividing by a negative number, we need to flip the inequality sign:

\[ k > -\frac{3}{2} \]

Now that we have the solution set \(k > -\frac{3}{2}\), we can determine which of the given values falls within that range:

• \(-5\) (is not greater than \(-\frac{3}{2}\))
• \(-32\) (is not greater than \(-\frac{3}{2}\))
• \(-1\) (is greater than \(-\frac{3}{2}\))
• \(-4\) (is not greater than \(-\frac{3}{2}\))

Thus, the value that falls in the solution set of the inequality is:

\(-1\) negative 1