Absolute value has how many solutions&nbsp;A ;2 B:3:C:4 D:5

Question

Absolute value has how many solutions&amp;nbsp;A ;2 B:3:C:4 D:5

karton · Accepted Answer

To determine the number of solutions for the absolute value, we need to consider the equation that involves the absolute value function.
The absolute value function, denoted as |x|, returns the distance of a number from zero on the number line. It always gives a non-negative result. The equation involving the absolute value can be written as:
|expression| = value
Now, let's analyze the given options:
A: 2
B: 3
C: 4
D: 5
To solve the equation |expression| = value, we have two cases to consider:
1. When the expression inside the absolute value is positive or zero:
In this case, the absolute value of the expression will be equal to the expression itself. Therefore, we can write:
expression = value
2. When the expression inside the absolute value is negative:
In this case, the absolute value of the expression will be equal to the negation of the expression. Therefore, we can write:
-expression = value
Now, let's apply these cases to the given options:
A: 2
For this option, we can have the equation:
expression = 2
This equation has a single solution.
B: 3
For this option, we can have the equation:
expression = 3
This equation also has a single solution.
C: 4
For this option, we can have two equations:
expression = 4
-expression = 4
These two equations give us two solutions.
D: 5
For this option, we can have two equations:
expression = 5
-expression = 5
These two equations also give us two solutions.
In summary:
Option A has 1 solution.
Option B has 1 solution.
Option C has 2 solutions.
Option D has 2 solutions.
Therefore, the correct answer is:

C: 4

, as it has two solutions.
Remember, this is a general explanation of how to determine the number of solutions for an absolute value equation. The actual number of solutions may vary depending on the specific equation provided.

Absolute value has how many solutions A ;2 B:3:C:4

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