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Solve for $t$ . $\newline$ $9 \geq t + 1 > -13$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $10 \geq t > -12$ $\newline$ (B) $8 \geq t > -12$ $\newline$ (C) $8 \geq t > -14$ $\newline$ (D) $10 \geq t > -14$

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Solve compound inequalities

Full solution

Q. Solve for

t

.

\newline

9 \geq t + 1 > -13

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

10 \geq t > -12

\newline

(B)

8 \geq t > -12

\newline

(C)

8 \geq t > -14

\newline

(D)

10 \geq t > -14

Analyze Compound Inequality: Analyze the given compound inequality. $\newline$ The inequality $9 \geq t + 1 > -13$ consists of two parts: $9 \geq t + 1$ and $t + 1 > -13$ . To solve for $t$ , we need to isolate $t$ in both parts of the inequality.
Isolate t (Part $1$ ): Isolate t in the first part of the inequality. $\newline$ Starting with $9 \geq t + 1$ , we need to subtract $1$ from both sides to isolate t. $\newline$ $9 - 1 \geq t + 1 - 1$ $\newline$ $8 \geq t$
Isolate t (Part $2$ ): Isolate $t$ in the second part of the inequality. $\newline$ Now, we look at the second part of the inequality, $t + 1 > -13$ . Similarly, we subtract $1$ from both sides to isolate $t$ . $\newline$ $t + 1 - 1 > -13 - 1$ $\newline$ $t > -14$
Combine Results: Combine the results to form the compound inequality. $\newline$ We have found that $8 \geq t$ and $t > -14$ . Combining these gives us the compound inequality: $\newline$ $8 \geq t > -14$
Check Answer Choices: Check the answer choices to see which one matches our solution. $\newline$ The correct answer choice should match the compound inequality $8 \geq t > -14$ .

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