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Explain Bot To order the variables a, b, c, and d based on the given inequalities, we need to compare the coefficients of each variable in the inequalities.
Let's analyze each inequality one by one:
1. c - 3 ≥ d
Here, we can rewrite the inequality in the form of c ≥ d + 3.
2. b + 4 < a + 1
By rearranging, we get b < a - 3.
3. a - 2 ≤ d - 7
Rearranging the inequality gives us a ≤ d - 5.
Now, let's compare the coefficients of the variables in these inequalities:
a: The second inequality, b < a - 3, means that a is larger than b + 3.
b: The second inequality, b < a - 3, tells us that b is less than a - 3.
c: There is only one inequality involving c, which is c ≥ d + 3.
d: The first inequality, c ≥ d + 3, indicates that d is smaller than c - 3. Additionally, the third inequality, a ≤ d - 5, shows that d is larger than a + 5.
Combining these comparisons, we can order the variables as follows:
b < a - 3 < c - 3 < d + 5
Hence, the order for a, b, c, and d is b, a, c, d.