<\/span><\/h2>\nYes, negative absolute value inequalities can have solutions.<\/strong> When an absolute value inequality involves a negative sign, it implies that the inequality is “strictly less than<\/strong>.” In such cases, the inequality might have a solution interval or be considered “empty.”<\/p>\nTo illustrate, let’s consider the inequality |-2x – 5| < -3. The negative sign before the constant -3 indicates that the absolute value expression must be strictly less than<\/strong> -3. However, an absolute value is always non-negative, meaning it is equal to or greater than zero. Therefore, it is impossible for the absolute value to be strictly less than -3, so this inequality does not have a solution. <\/p>\nIn similar cases, when a negative absolute value expression is compared to a positive constant, the inequality will never be satisfied. As a result, negative absolute value inequalities typically do not have solutions.<\/p>\n