Which compound inequality is equivalent to start absolute value A x minus b end absolute value is greater than c for all real numbers A , b , and c , where c is greater than or equal to 0 ?
Answer
A
negative c is less than A x minus b comma A x minus b is greater than c
B
A x minus b is less than negative c or A x minus b is greater than c
C
A x minus b is greater than negative c or A x minus b is greater than c
D
negative c is greater than A x minus b comma A x minus b is greater than c
Explanation
For any expression y, |y| > c (with c ≥ 0) means y is more than c units from 0. Thus y < −c or y > c. Substituting y = Ax − b gives Ax − b < −c or Ax − b > c, which is choice B.
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