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Solve for $f$ . $\newline$ $f - 2 \geq 7$ or $f - 12 \leq -6$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $f > 9$ or $f \leq 6$ $\newline$ (B) $f \geq 9$ or $f < 6$ $\newline$ (C) $f > 9$ or $f < 6$ $\newline$ (D) $f \geq 9$ or $f \leq 6$

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Solve compound inequalities

Full solution

Q. Solve for

f

.

\newline

f - 2 \geq 7

or

f - 12 \leq -6

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

f > 9

or

f \leq 6

\newline

(B)

f \geq 9

or

f < 6

\newline

(C)

f > 9

or

f < 6

\newline

(D)

f \geq 9

or

f \leq 6

Add $2$ to isolate $f$ : We have two inequalities to solve: $f - 2 \geq 7$ and $f - 12 \leq -6$ . Let's start with the first inequality $f - 2 \geq 7$ . $\newline$ To isolate $f$ , we need to add $2$ to both sides of the inequality. $\newline$ $f - 2 + 2 \geq 7 + 2$ $\newline$ $f \geq 9$
Add $12$ to isolate f: Now let's solve the second inequality $f - 12 \leq -6$ . To isolate $f$ , we need to add $12$ to both sides of the inequality. $f - 12 + 12 \leq -6 + 12$ $f \leq 6$
Combine solutions with OR: We have found the solutions to both inequalities. Now we need to combine them using the ＂or＂ operator as given in the original compound inequality. $\newline$ The final compound inequality is: $\newline$ $f \geq 9$ or $f \leq 6$

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