Solve for a. a - 1 ≥ 9 or a + 7 ≤ 15 Write your answer as a compound inequality with integers. Choices: (A)a > 10 or a 10 or a ≤ 8 (D)a ≥ 10 or a ≤ 8

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

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

a

\newline

a - 1 \geq 9

a + 7 \leq 15

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

a > 10

a < 8

\newline

(B)

a \geq 10

a < 8

\newline

(C)

a > 10

a \leq 8

\newline

(D)

a \geq 10

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 $a \leq 8$ .