Solve for a. a + 3 ≤ 11 or a - 14 ≥ 1 Write your answer as a compound inequality with integers. Choices: (A)a ≤ 14 or a ≥ -13 (B)a ≤ 14 or a ≥ 15 (C)a ≤ 8 or a ≥ 15 (D)a ≤ 8 or a ≥ -13

Solve First Part: Solve the first part of the compound inequality. We have a + 3 ≤ 11. To isolate a, we need to subtract 3 from both sides of the inequality. a + 3 - 3 ≤ 11 - 3 a ≤ 8Solve Second Part: Solve the second part of the compound inequality. We have a - 14 ≥ 1. To isolate a, we need to add 14 to both sides of the inequality. a - 14 + 14 ≥ 1 + 14 a ≥ 15Combine Solutions: Combine the solutions from Step 1 and Step 2 to write the final compound inequality. The solution is a ≤ 8 or a ≥ 15.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

a

\newline

a + 3 \leq 11

a - 14 \geq 1

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

a \leq 14

a \geq -13

\newline

(B)

a \leq 14

a \geq 15

\newline

(C)

a \leq 8

a \geq 15

\newline

(D)

a \leq 8

a \geq -13

Solve First Part: Solve the first part of the compound inequality. $\newline$ We have $a + 3 \leq 11$ . To isolate $a$ , we need to subtract $3$ from both sides of the inequality. $\newline$ $a + 3 - 3 \leq 11 - 3$ $\newline$ $a \leq 8$
Solve Second Part: Solve the second part of the compound inequality. $\newline$ We have $a - 14 \geq 1$ . To isolate $a$ , we need to add $14$ to both sides of the inequality. $\newline$ $a - 14 + 14 \geq 1 + 14$ $\newline$ $a \geq 15$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $a \leq 8$ or $a \geq 15$ .