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What inequality represents this interval? $\newline$ $(-\infty, -1)$ $\newline$ Choices: $\newline$ (A) $x > -1$ $\newline$ (B) $x \geq -1$ $\newline$ (C) $x < -1$ $\newline$ (D) $x \leq -1$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-\infty, -1)

\newline

Choices:

\newline

(A)

x > -1

\newline

(B)

x \geq -1

\newline

(C)

x < -1

\newline

(D)

x \leq -1

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval is $(-\infty, -1)$ , which means that the endpoints are $-\infty$ and $-1$ . Since the interval notation uses parentheses, neither endpoint is included in the interval.
Determine Direction: Determine the direction of the inequality. Since the interval extends from negative infinity up to but not including $-1$ , the inequality must indicate that $x$ is less than $-1$ .
Choose Inequality Symbol: Choose the correct inequality symbol. The inequality must be ＂less than＂ because $-1$ is not included in the interval. Therefore, the correct symbol is ＂ $<$ ＂.
Write Inequality: Write the inequality that represents the interval. The correct inequality is $x < -1$ , which corresponds to choice $(C)$ .

More problems from Interval notation

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

S = \{2, 12\}

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

\newline

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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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\{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)

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[D](-\infty,-3]

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\newline

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A physicist measures the energies of atoms

A

B

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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

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