Answer:
x=71/9, 55/9
Explanation:
Pre-Solving
Given
We are given the absolute value equation 9|x-7| + 9 = 17, and we want to solve the equation for x.
Solving
First, we need to isolate the absolute value on one side of the equation.
To do this, we can first subtract 9 from both sides.
9|x-7| + 9 = 17
-9 -9
____________________
9|x-7| = 8
Now, we divide both sides by 9.
|x-7| = 8/9
For absolute value equations, there are two cases; one case is when the expression (or number) that the absolute value expression is equal to is positive, and the other is when it is negative.
This means we need to split the equation into 2 cases.
The first case is when 8/9 (the number the absolute value expression is equal to) is positive.
x - 7 = 8/9
Add 7 to both sides.
x = 71/9
The second case is when 8/9 is negative.
x - 7 = -8/9
Add 7 to both sides.
x = 55/9
The solution is:
x = 71/9, 55/9