Question

|7x+5| + 3 > 0

Explanation:

Step1: Recall absolute value property

The absolute value of any real number \( a \), denoted \( |a| \), is always non - negative, i.e., \( |a|\geq0 \) for all real numbers \( a \). So for \( |7x + 5| \), we have \( |7x+5|\geq0 \) for all real values of \( x \).

Step2: Analyze the left - hand side of the inequality

We are given the inequality \( |7x + 5|+3>0 \). Since \( |7x + 5|\geq0 \), then \( |7x + 5|+3\geq0 + 3=3 \).

Step3: Determine the solution set

Since \( |7x + 5|+3\geq3 \), and \( 3>0 \), the inequality \( |7x + 5|+3>0 \) is true for all real numbers \( x \).

Answer:

All real numbers \( x\in\mathbb{R} \) (or \( (-\infty,\infty) \))