Solve and express in interval notation

The answers are correct.

To represent disjoint intervals in interval notation, we only need to join each interval using a "union sign", or ∪.
So the required answer would be:
(-∞, -3/4) ∪ (2, +∞)
Parentheses have been used in the above cases (instead of square brackets) because in each of the 4 cases, the values of the limits are to be excluded from the interval.

Thank you!

You're welcome!

To express the solutions in interval notation, we can break down the separate intervals and write them in a concise format.

For the inequality |5 – 8x| > 11, you found the solutions x < -3/4 or x > 2. To express this in interval notation, we can write it as the union of two intervals: (-∞, -3/4) ∪ (2, ∞).

For the inequality (x-3)/(x^2-25) < 0, you found the solutions x < -5 or 3 < x < 5. To express this in interval notation, we can write it as the intersection of two intervals: (-∞, -5) ∩ (3, 5).