Option D: 4 is correct since at x = 4, the inequality stays true, and not for any other options.
Given that:
The given inequality containing variable x is: [tex]x + 9 < 4x[/tex]
Options given have values 1, 2, 3 and 4.
Evaluating LHS(Left Hand Side) = x + 9 and RHS(Right Hand side) = 4x of inequality for all cases:
Checking all cases:
Case 1: x + 1
LHS = x + 9 = 1 + 9 = 10
RHS = 4x = 4
Thus: LHS > RHS
Case 1: x = 2
LHS = x + 9 = 2 + 9 = 11
RHS = 4x = 8
Thus: LHS > RHS
Case 1: x = 3
LHS = x + 9 = 3 + 9 = 12
RHS = 4x = 12
Thus: LHS = RHS
Case 1: x = 4
LHS = x + 9 = 13 + 9 = 10
RHS = 4x = 16
Thus: LHS < RHS
Thus, the inequality x + 9 < 4x is true only for case when x = 4.
Thus, option D: 4 is correct value for which the given inequality stays true.
Learn more about inequalities here:
https://brainly.com/question/19491153
