Answer :
Final answer:
To solve the compound inequality [-6x + 14 < -28 or 9x + 15 ≤ -12], we solve each inequality individually. The first inequality gives us x > 7, and the second gives us x ≤ -3. Since it's an 'or' statement and both solutions don't overlap, the answer is x > 7.
Explanation:
To solve the compound inequality [-6x + 14 < -28 or 9x + 15 ≤ -12], we need to split it into two separate inequalities and solve each one individually.
First, let's solve -6x + 14 < -28:
- Add -14 to both sides: -6x < -42
- Divide by -6, remembering to reverse the inequality: x > 7
Now, let's solve 9x + 15 ≤ -12:
- Subtract 15 from both sides: 9x ≤ -27
- Divide by 9: x ≤ -3
Since we are dealing with an 'or' statement, we take the union of both solutions.
The first inequality gives us x > 7, which is not satisfied by any values that satisfy the second inequality x ≤ -3.
Therefore, the correct answer is (a) ( x > 7 ) because this is the only solution that cannot overlap with the solution to the second inequality.
