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Solve for $a$ . $\newline$ $a - 1 \geq 9$ or $a + 7 \leq 15$ $\newline$ Write your answer as a compound inequality with integers. $\newline$ Choices: $\newline$ (A) $a > 10$ or $a < 8$ $\newline$ (B) $a \geq 10$ or $a < 8$ $\newline$ (C) $a > 10$ or $a \leq 8$ $\newline$ (D) $a \geq 10$ or $a \leq 8$

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Solve compound inequalities

Full solution

Q. Solve for

a

.

\newline

a - 1 \geq 9

or

a + 7 \leq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

a > 10

or

a < 8

\newline

(B)

a \geq 10

or

a < 8

\newline

(C)

a > 10

or

a \leq 8

\newline

(D)

a \geq 10

or

a \leq 8

Add $1$ to isolate $a$ : To solve the inequality $a - 1 \geq 9$ , we need to isolate $a$ by adding $1$ to both sides of the inequality. $\newline$ $a - 1 + 1 \geq 9 + 1$ $\newline$ $a \geq 10$
Subtract $7$ to isolate $a$ : To solve the inequality $a + 7 \leq 15$ , we need to isolate $a$ by subtracting $7$ from both sides of the inequality. $\newline$ $a + 7 - 7 \leq 15 - 7$ $\newline$ $a \leq 8$
Combine inequalities: Now we combine the two inequalities to form the compound inequality. $\newline$ The solution is $a \geq 10$ or $a \leq 8$ .

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