QuestionSolve the following absolute value equations or state if there is no solution:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Studdy Solution
STEP 1
Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, it is always non-negative.
. If , then or .
Now, let's solve each equation one by one.
STEP 2
olving .
The absolute value equation can be written as two separate equations and .
STEP 3
olving gives .
olving gives .
STEP 4
olving .
The absolute value equation can be written as two separate equations and .
STEP 5
olving gives and .
olving gives and .
STEP 6
olving .
The absolute value equation can be written as two separate equations and .
STEP 7
olving gives .
olving gives .
STEP 8
olving .
First, divide both sides by2 to isolate the absolute value. This gives .
The absolute value equation can be written as two separate equations and .
STEP 9
olving gives and .
olving gives and .
The solutions for the remaining equations can be found in a similar manner.
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