High School

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Solve the compound inequality:

\[ 6 - x > 15 \] or \[ 2x - 9 \geq 3 \]

A. \( x > 9 \) or \( x \leq 6 \)
B. \( x < 9 \) or \( x \geq -6 \)
C. \( x > -9 \) or \( x \leq -6 \)
D. \( x < -9 \) or \( x \geq 6 \)

Answer :

Final answer:

To solve the compound inequality, solve each inequality separately and find the intersection of their solutions. The intersection of the solutions to the given compound inequality is x < -9 or x ≥ 6.

Explanation:

To solve the compound inequality 6 - x > 15 or 2x - 9 ≥ 3, we need to solve each inequality separately and find the intersection of their solutions. Let's solve the first inequality, 6 - x > 15:

6 - x > 15

-x > 15 - 6

-x > 9

x < -9

Now let's solve the second inequality, 2x - 9 ≥ 3:

2x - 9 ≥ 3

2x ≥ 3 + 9

2x ≥ 12

x ≥ 6

The intersection of the solutions is x < -9 or x ≥ 6. Therefore, the correct answer is choice D. x < -9 or x ≥ 6.

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Rewritten by : Barada

Final answer:

To solve the compound inequality, solve each inequality separately and then combine the solutions. The solution is x < -9 or x ≥ 6 that is option D is correct.

Explanation:

To solve the compound inequality, we need to solve each inequality separately and then combine the solutions. Let's start with the first inequality, 6 - x > 15. Subtracting 6 from both sides, we get -x > 9. Multiplying both sides by -1 and reversing the inequality, we have x < -9. Next, let's solve the second inequality, 2x - 9 ≥ 3. Adding 9 to both sides, we get 2x ≥ 12. Dividing both sides by 2, we have x ≥ 6. Combining the solutions, we have x < -9 or x ≥ 6. Therefore, the correct answer is option D: x < -9 or x ≥ 6.