3 + 4I 3x + 7 I ≥ -89
4I 3x + 7 I ≥ -89 - 3 (Subtracting 3 on both sides of the inequality)
4I 3x + 7 I ≥ -92 (Adding like terms)
I 3x + 7 I ≥ -92/4 (Dividing by 4 on both sides of the inequality)
I 3x + 7 I ≥ -23
Separating the inequality into two inequalities , we have:
3x + 7 ≥ -23 (Inequality 1) and -(3x + 7) ≥ -23 (Inequality 2)
Inequality 1:
3x + 7 ≥ -23
3x ≥ -23 - 7 (Subtracting 7 on both sides of the inequality)
3x ≥ - 30 (Adding like terms)
x ≥ - 30/3 (Dividing by 4 on both sides of the inequality)
x ≥ -10 (Dividing)
Inequality 2:
-(3x + 7) ≥ -23
-3x - 7 ≥ -23 (Distributing)
-3x ≥ -23 + 7 (Adding 7 on both sides of the inequality)
-3x ≥ -16 (Subtracting)
x ≤ -16/-3 (Dividing by -3 on both sides of the inequality)
x ≤ 16/3 (Using the sign rules)
The graph would be:
We see that all real numbers satisfy the inequality.