What is the complete set of values of x for which 100 − 99x ≤ 98 − 97x and 96 + 95x > 94 + 93x ?
A) −1 < x ≤ 1
B) x ≤ −1 or x > 1
C) x ≥ 1
D) x > −1
E) x > 1
IMAT 2023 · Question 53
Q53 - Algebraic inequalities
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The correct answer is C) x ≥ 1.
First inequality: 100 − 99x ≤ 98 − 97x → 2 ≤ 2x → x ≥ 1.
Second: 96 + 95x > 94 + 93x → 2x > −2 → x > −1.
Both have to hold, and every x ≥ 1 is already greater than −1, so x ≥ 1.
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