Solve for j. j + 14 ≤ 5 or j + 5 ≥ 12 Write your answer as a compound inequality with integers. Choices: (A)j ≤ 19 or j ≥ 7 (B)j ≤ 19 or j ≥ 17 (C)j ≤ -9 or j ≥ 7 (D)j ≤ -9 or j ≥ 17

Solve First Part: Solve the first part of the compound inequality. We have j + 14 ≤ 5. To isolate j, we need to subtract 14 from both sides of the inequality. j + 14 - 14 ≤ 5 - 14 j ≤ -9Solve Second Part: Solve the second part of the compound inequality. We have j + 5 ≥ 12. To isolate j, we need to subtract 5 from both sides of the inequality. j + 5 - 5 ≥ 12 - 5 j ≥ 7Combine Solutions: Combine the solutions from Step 1 and Step 2 to write the final compound inequality. The solution is j ≤ -9 or j ≥ 7.

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Math Problems

Algebra 1

Solve compound inequalities

Full solution

Q. Solve for

j

\newline

j + 14 \leq 5

j + 5 \geq 12

\newline

Write your answer as a compound inequality with integers.

\newline

Choices:

\newline

(A)

j \leq -9

j \geq 7

\newline

(B)

j \leq -9

j \geq 17

\newline

(C)

j \leq 19

j \geq 7

\newline

(D)

j \leq 19

j \geq 17

Solve First Part: Solve the first part of the compound inequality. $\newline$ We have $j + 14 \leq 5$ . To isolate $j$ , we need to subtract $14$ from both sides of the inequality. $\newline$ $j + 14 - 14 \leq 5 - 14$ $\newline$ $j \leq -9$
Solve Second Part: Solve the second part of the compound inequality. $\newline$ We have $j + 5 \geq 12$ . To isolate $j$ , we need to subtract $5$ from both sides of the inequality. $\newline$ $j + 5 - 5 \geq 12 - 5$ $\newline$ $j \geq 7$
Combine Solutions: Combine the solutions from Step $1$ and Step $2$ to write the final compound inequality. $\newline$ The solution is $j \leq -9$ or $j \geq 7$ .