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What inequality represents this interval? $\newline$ $(-\infty, 0)$ $\newline$ Choices: $\newline$ (A) $x < 0$ $\newline$ (B) $x > 0$ $\newline$ (C) $x \geq 0$ $\newline$ (D) $x \leq 0$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-\infty, 0)

\newline

Choices:

\newline

(A)

x < 0

\newline

(B)

x > 0

\newline

(C)

x \geq 0

\newline

(D)

x \leq 0

Identify Endpoints: Identify the endpoints of the interval $-\infty, 0$ . The endpoints are $-\infty$ and $0$ .
Determine Inclusion: Determine whether the finite endpoint $0$ is included in the interval. Since the interval is open at $0$ (indicated by the parenthesis), $0$ is not included in the interval.
Choose Correct Inequality: Choose the correct inequality that represents the interval. Since the interval extends from negative infinity up to, but not including, $0$ , the inequality must express that $x$ is less than $0$ .
Match with Choices: Match the correct inequality with the given choices. The inequality that represents the interval $(-\infty, 0)$ is $x < 0$ , which corresponds to choice $(A)$ .

More problems from Interval notation

Question

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

S = \{2, 12\}

R \cup S

\newline

\newline

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

\newline

\Phi

\newline

\{2, 4, 12\}

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\{-4, 2\}

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Which is the set of integers greater than or equal to

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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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(D)\{1,6\}

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\newline

\newline

\{x|x = -13\}

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\{x|x < -13\}

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\{x|x > -13\}

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\{x|x \leq -13\}

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What interval does this inequality represent?

\newline

\newline

[A](-3,\infty)

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[B](-3,\infty)

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[C](-\infty,-3)

\newline

[D](-\infty,-3]

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\newline

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106 \times 37 \div 10,000

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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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