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What inequality represents this interval? $\newline$ $(-\infty, -2]$ $\newline$ Choices: $\newline$ (A) $x < -2$ $\newline$ (B) $x \leq -2$ $\newline$ (C) $x > -2$ $\newline$ (D) $x \geq -2$

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Interval notation

Full solution

Q. What inequality represents this interval?

\newline

(-\infty, -2]

\newline

Choices:

\newline

(A)

x < -2

\newline

(B)

x \leq -2

\newline

(C)

x > -2

\newline

(D)

x \geq -2

Identify Endpoints: Identify the endpoints of the interval and whether they are included in the set. The interval $(-\infty, -2]$ has $-\infty$ as the lower bound and $-2$ as the upper bound. The square bracket at $-2$ indicates that $-2$ is included in the interval.
Determine Inequality: Determine the inequality that corresponds to the interval. Since $-\infty$ is not a number that can be reached, it is not included, and the inequality will not have an equal sign for the lower bound. However, because $-2$ is included, the inequality must have an equal sign for $-2$ .
Choose Symbol: Choose the correct inequality symbol. The interval extends from $-\infty$ up to and including $-2$ , which means the values that $x$ can take are less than or equal to $-2$ .
Match Inequality: Match the correct inequality with the given choices. The inequality that represents the interval -\infty, -2]\ is \＂\$x \leq -2\＂.

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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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\newline

1

\newline

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

\newline

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

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