Question

Which compound inequality is equivalent to (a ⋅ x - b > C) for all real numbers a, b, and c, where (c ≠ 0)?

a) C < ax - b
b) ax - b > -C
c) ax - b > C
d) ax - b < -C

Answer 1

The equivalent compound inequality to the given inequality (a · x - b > C) is option c) ax - b > C, as it exactly matches the original inequality without any transformations.

Step-by-step explanation:

The question involves finding an equivalent compound inequality for the inequality (a · x - b > C) given the conditions that all the variables are real numbers and (c ≠ 0). By analyzing the options provided, option c) ax - b > C is the correct equivalent inequality. This is because, in option c), the inequality already exactly matches the given inequality, indicating the inequality is kept intact and no transformations have been applied to the original variables.