Answer :
The solution to the given inequality is x ≤ 36.35.
To solve the given inequality, we can follow these steps:
1. Subtract 38.8 from both sides of the inequality: 2x - 38.8 ≥ 110.5 - 38.8
This simplifies to 2x - 38.8 ≥ 71.7.
2. Add 38.8 to both sides of the inequality: 2x ≥ 71.7 + 38.8
This simplifies to 2x ≥ 110.5.
3. Divide both sides of the inequality by 2: (2x)/2 ≥ 110.5/2
This simplifies to x ≥ 55.25.
Therefore, the solution to the inequality is x ≥ 55.25. However, we need to consider the original inequality, which is -1 + 2x - 38.8 ≥ 110.5. We can see that the term "-1 + 2x" represents a negative value, so it will decrease the left side of the inequality. In order to maintain the inequality, we need to find the upper bound for x.
To find the upper bound, we set -1 + 2x - 38.8 equal to 110.5:
-1 + 2x - 38.8 = 110.5
2x - 39.8 = 110.5
2x = 150.3
x = 75.15
Therefore, x must be less than or equal to 75.15 in order to satisfy the original inequality.
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