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Solve for $z$ . $\newline$ $z + 13 > 12$ or $z + 19 \leq 7$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $-1 > z \geq -12$ $\newline$ (B) $-1 \geq z \geq -12$ $\newline$ (C) $z \geq -1$ or $z \leq -12$ $\newline$ (D) $z > -1$ or $z \leq -12$

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Solve compound inequalities

Full solution

Q. Solve for

z

.

\newline

z + 13 > 12

or

z + 19 \leq 7

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

-1 > z \geq -12

\newline

(B)

-1 \geq z \geq -12

\newline

(C)

z \geq -1

or

z \leq -12

\newline

(D)

z > -1

or

z \leq -12

First Inequality Solution: We have two inequalities to solve: $z + 13 > 12$ and $z + 19 \leq 7$ . Let's start with the first inequality $z + 13 > 12$ . $\newline$ To isolate $z$ , we need to subtract $13$ from both sides of the inequality. $\newline$ $z + 13 - 13 > 12 - 13$ $\newline$ $z > -1$
Second Inequality Solution: Now let's solve the second inequality $z + 19 \leq 7$ . $\newline$ To isolate $z$ , we need to subtract $19$ from both sides of the inequality. $\newline$ $z + 19 - 19 \leq 7 - 19$ $\newline$ $z \leq -12$
Combining Inequalities: We now have two parts of the compound inequality: $z > -1$ and $z \leq -12$ . Since the original statement uses ＂or,＂ we combine these two inequalities using ＂or.＂ $\newline$ $z > -1$ or $z \leq -12$

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