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What inequality represents this interval? $\newline$ $[2, 10]$ $\newline$ Choices: $\newline$ (A) $2 < x < 10$ $\newline$ (B) $2 < x \leq 10$ $\newline$ (C) $2 \leq x < 10$ $\newline$ (D) $2 \leq x \leq 10$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

[2, 10]

\newline

Choices:

\newline

(A)

2 < x < 10

\newline

(B)

2 < x \leq 10

\newline

(C)

2 \leq x < 10

\newline

(D)

2 \leq x \leq 10

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval $[2, 10]$ has endpoints $2$ and $10$ , and the square brackets indicate that both endpoints are included in the interval.
Translate to Inequality: Translate the interval notation into an inequality. Since both endpoints are included, the inequality must use ＂less than or equal to＂ for both endpoints. This means the inequality will be of the form $2 \leq x \leq 10$ .
Match with Choices: Match the correct inequality with the given choices. The inequality $2 \leq x \leq 10$ corresponds to choice (D).

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

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A physicist measures the energies of atoms

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b

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

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B

\newline

1

\newline

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

\newline

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