Answer:
|-2x - 5| > 5 is x < -5 or x > 0
Explanation:
|2y + 3| < 19:
To solve this inequality, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2y + 3 > 0
In this case, the absolute value simplifies to 2y + 3 < 19.
Solving this inequality, we get 2y < 16 and y < 8.
Case 2: 2y + 3 < 0
In this case, the absolute value simplifies to -(2y + 3) < 19.
Solving this inequality, we get -2y < 22 and y > -11.
Therefore, the solution set for the inequality |2y + 3| < 19 is -11 < y < 8.
|2s - 6| < 6:
Again, we'll consider two cases based on the sign of the expression inside the absolute value.
Case 1: 2s - 6 > 0
In this case, the absolute value simplifies to 2s - 6 < 6.
Solving this inequality, we get 2s < 12 and s < 6.
Case 2: 2s - 6 < 0
In this case, the absolute value simplifies to -(2s - 6) < 6.
Solving this inequality, we get -2s < 12 and s > -6.
Therefore, the solution set for the inequality |2s - 6| < 6 is -6 < s < 6.
|5 - x| < 4:
Case 1: 5 - x > 0
In this case, the absolute value simplifies to 5 - x < 4.
Solving this inequality, we get -x < -1 and x > 1.
Case 2: 5 - x < 0
In this case, the absolute value simplifies to -(5 - x) < 4.
Solving this inequality, we get x < 9 and x < 5.
Therefore, the solution set for the inequality |5 - x| < 4 is 1 < x < 5.
|5t - 1| > 21:
Case 1: 5t - 1 > 0
In this case, the absolute value simplifies to 5t - 1 > 21.
Solving this inequality, we get 5t > 22 and t > 4.4.
Case 2: 5t - 1 < 0
In this case, the absolute value simplifies to -(5t - 1) > 21.
Solving this inequality, we get -5t > 20 and t < -4.
Therefore, the solution set for the inequality |5t - 1| > 21 is t < -4 or t > 4.4.
|-2x - 5| > 5:
Case 1: -2x - 5 > 0
In this case, the absolute value simplifies to -2x - 5 > 5.
Solving this inequality, we get -2x > 10 and x < -5.
Case 2: -2x - 5 < 0
In this case, the absolute value simplifies to -(-2x - 5) > 5.
Solving this inequality, we get 2x > 0 and x > 0.
Therefore, the solution set for the inequality |-2x - 5| > 5 is x < -5 or x > 0.