QuestionБодлого 8. модультай тэгшитгэлийг бодно уу. A) -6 B) 4 C) D) шийдгуй
Studdy Solution
STEP 1
1. The equation involves absolute values: .
2. We need to consider different cases based on the critical points where the expressions inside the absolute values change sign.
STEP 2
1. Identify critical points and define intervals.
2. Solve the equation for each interval.
3. Check solutions against the original equation.
STEP 3
Identify the critical points where the expressions inside the absolute values change sign. These points are and .
STEP 4
Define the intervals based on the critical points: - Interval 1: - Interval 2: - Interval 3:
STEP 5
Solve the equation for each interval.
**Interval 1: **
In this interval, both expressions inside the absolute values are negative, so:
The equation becomes:
**Interval 2: **
In this interval, is non-negative and is negative, so:
The equation becomes:
This is a contradiction, so there is no solution in this interval.
**Interval 3: **
In this interval, both expressions inside the absolute values are non-negative, so:
The equation becomes:
STEP 6
Check the solutions against the original equation and the intervals:
- is in Interval 1, which is valid.
- is in Interval 3, which is valid.
The solutions are:
Therefore, the correct answer is:
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