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Solve the compound inequality:

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

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 :

Sure! Let's solve the compound inequality step-by-step:

We have two separate inequalities to solve:

1. [tex]\( 6 - x > 15 \)[/tex]
2. [tex]\( 2x - 9 \geq 3 \)[/tex]

### Solving the first inequality: [tex]\( 6 - x > 15 \)[/tex]

1. Subtract 6 from both sides:
[tex]\[
-x > 15 - 6
\][/tex]
[tex]\[
-x > 9
\][/tex]

2. Multiply by -1 and reverse the inequality sign:
[tex]\[
x < -9
\][/tex]

### Solving the second inequality: [tex]\( 2x - 9 \geq 3 \)[/tex]

1. Add 9 to both sides:
[tex]\[
2x \geq 3 + 9
\][/tex]
[tex]\[
2x \geq 12
\][/tex]

2. Divide by 2:
[tex]\[
x \geq 6
\][/tex]

### Combine the solutions:

The compound inequality uses "or," which means we combine the solutions from both inequalities:

- From [tex]\( 6 - x > 15 \)[/tex], we have [tex]\( x < -9 \)[/tex].
- From [tex]\( 2x - 9 \geq 3 \)[/tex], we have [tex]\( x \geq 6 \)[/tex].

Thus, the solution is [tex]\( x < -9 \)[/tex] or [tex]\( x \geq 6 \)[/tex].

### Choose the correct option:

The correct answer is option D [tex]\( x < -9 \)[/tex] or [tex]\( x \geq 6 \)[/tex].

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