Question

1. $-5|x-3|-5<15$

solution(s):

Explanation:

Step1: Isolate absolute value term

$-5|x-3| - 5 < 15$
Add 5 to both sides:
$-5|x-3| < 20$

Step2: Divide by negative constant

Divide both sides by -5, reverse inequality:
$|x-3| > -4$

Step3: Analyze absolute value property

Absolute value is always non-negative, so $|x-3| \geq 0$ for all real $x$. Since $0 > -4$, the inequality holds for all real numbers.

Answer:

All real numbers, or in interval notation: $(-\infty, \infty)$