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What inequality represents this interval? $\newline$ $[-4, \infty)$ $\newline$ Choices: $\newline$ (A) $x > -4$ $\newline$ (B) $x < -4$ $\newline$ (C) $x \leq -4$ $\newline$ (D) $x \geq -4$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

[-4, \infty)

\newline

Choices:

\newline

(A)

x > -4

\newline

(B)

x < -4

\newline

(C)

x \leq -4

\newline

(D)

x \geq -4

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval is $[-4, \infty)$ , which means $-4$ is included (as indicated by the square bracket) and $\infty$ is not included (as indicated by the parenthesis).
Determine Inequality: Determine the inequality that corresponds to the interval. Since $-4$ is included, the inequality must use either $\leq$ (less than or equal to) or $\geq$ (greater than or equal to). Since the interval extends to positive infinity, the inequality must allow for all numbers greater than or equal to $-4$ .
Match Correct Inequality: Match the correct inequality with the given choices. The interval [-4, \infty)\] corresponds to the inequality \$x \geq -4, which means that $x$ is greater than or equal to $-4$ .

More problems from Interval notation

Question

R = \{-4, 4, 14\}

S = \{2, 12\}

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\newline

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\{-4,2,4,12,14\}

\newline

\Phi

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\{2, 4, 12\}

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\newline

(A)\{1,2,3,4,5,6\}

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(B)\{0,1,2,3,4,5,6\}

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(C)\{\text{null set}\}

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Which is the set of numbers less than

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\newline

\{x|x = -13\}

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\{x|x \leq -13\}

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What interval does this inequality represent?

\newline

\newline

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[B](-3,\infty)

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\newline

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Question

A physicist measures the energies of atoms

A

B

to be the positive values

a

b

respectively. He determines that the energy of atom

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is between one percent more than and one percent less than twice the energy of atom

A

. Which of the following systems of inequalities best models the possible range of values for the energies of atoms

A

B

\newline

1

\newline

\left\{\begin{array}{l}a<2.02 b \\ a>1.98 b\end{array}\right.

\newline

\left\{\begin{array}{l}a<2 b+0.02 \\ a>2 b-0.02\end{array}\right.

\newline

\left\{\begin{array}{l}b<2.02 a \\ b>1.98 a\end{array}\right.

\newline

\left\{\begin{array}{l}b<2 a+0.02 \\ b>2 a-0.02\end{array}\right.

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Question

2+2(8347-4783)=-2 j

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