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Solve for $k$ . $\newline$ $k - 13 > 2$ or $k + 20 < 19$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $15 > k > -1$ $\newline$ (B) $15 \geq k > -1$ $\newline$ (C) $k > 15$ or $k < -1$ $\newline$ (D) $k \geq 15$ or $k < -1$

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Solve compound inequalities

Full solution

Q. Solve for

k

.

\newline

k - 13 > 2

or

k + 20 < 19

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

15 > k > -1

\newline

(B)

15 \geq k > -1

\newline

(C)

k > 15

or

k < -1

\newline

(D)

k \geq 15

or

k < -1

Solve First Part: Solve the first part of the compound inequality. $\newline$ We have $k - 13 > 2$ . To isolate $k$ , we need to add $13$ to both sides of the inequality. $\newline$ $k - 13 + 13 > 2 + 13$ $\newline$ $k > 15$
Solve Second Part: Solve the second part of the compound inequality. $\newline$ We have $k + 20 < 19$ . To isolate $k$ , we need to subtract $20$ from both sides of the inequality. $\newline$ $k + 20 - 20 < 19 - 20$ $\newline$ $k < -1$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to form the compound inequality. $\newline$ The solutions are $k > 15$ or $k < -1$ .

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