Thank you for visiting Choose the correct linear inequality for the depth of the hole A tex 180 30 25 x 3 330 tex B tex 180 leq 30. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve the given linear inequality for the depth of the hole, let's analyze the options one by one. We're looking for an inequality that correctly represents some boundary conditions related to the depth of a hole.
The general form provided in the inequalities is:
[tex]30 + 25 (x - 3)[/tex]
This expression represents the depth of the hole, where [tex]x[/tex] might represent some variable like time or another measure influencing the depth.
Option Analysis:
Option (a):
[tex]180 < 30 + 25 (x - 3) < 330[/tex]
This option suggests that the depth of the hole is greater than 180 and less than 330. This double inequality includes the boundaries correctly if they represent the minimum and maximum depth.
Option (b):
[tex]180 \leq 30 + 25 (x - 3) \leq 330[/tex]
This version uses the inclusive inequality with [tex]\leq[/tex]. It means the depth can be exactly 180 or 330, making it more inclusive than option (a).
Option (c):
[tex]330 < 30 + 25 (x - 3) \leq 180[/tex]
This is incorrect as it implies that 330 is less than the expression, but at the same time the expression is less than or equal to 180, which is not possible.
Option (d):
[tex]330 < 30 + 25 (x - 3) < 180[/tex]
Like option (c), this is logically inconsistent because 330 is greater than 180. Therefore, it cannot be simultaneously greater than 30 + 25 (x - 3) when it is supposed to be less than 180.
Conclusion:
The correct answer is option (b):
[tex]180 \leq 30 + 25 (x - 3) \leq 330[/tex]
This choice properly sets a range for the depth, allowing the boundary values to be included. Thus, the depth of the hole is between 180 and 330 inclusive.
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Rewritten by : Jeany
