To solve the inequality \( 4a - 17 > 3 \) or \( 9a - 8 < 10 \), we will solve each part separately.
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For the first inequality: \[ 4a - 17 > 3 \] Add 17 to both sides: \[ 4a > 3 + 17 \] \[ 4a > 20 \] Now, divide by 4: \[ a > 5 \]
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For the second inequality: \[ 9a - 8 < 10 \] Add 8 to both sides: \[ 9a < 10 + 8 \] \[ 9a < 18 \] Now, divide by 9: \[ a < 2 \]
Now we have two separate inequalities:
- \( a > 5 \)
- \( a < 2 \)
The solution is \( a < 2 \) or \( a > 5 \).
In interval notation, this can be expressed as: \[ (-\infty, 2) \cup (5, \infty) \]
As a compound inequality with integers, we express it as: \[ a < 2 \quad \text{or} \quad a > 5 \]
This is the final answer.