How do you solve 8-3|p-4|=2?
I got 6 and 2 as an answer
8 - 3 |x| = 2
- 3 |x| = -6
|x| = 2
x = + 2 or x = -2
so
p-4 = 2 so p = 6
p-4 = -2 so p = 2
I agree with you.
Thank you
You are welcome.
To solve the equation 8-3|p-4|=2, we need to isolate the variable p. Here are the steps:
1. Start by isolating the absolute value expression. To do this, subtract 8 from both sides of the equation:
8 - 8 - 3|p-4| = 2 - 8
-3|p-4| = -6
2. Divide both sides of the equation by -3 to isolate the absolute value expression:
-3|p-4| / -3 = -6 / -3
|p-4| = 2
3. Now, consider two cases: p - 4 is positive or negative within the absolute value:
Case 1: (p-4) is positive:
If (p-4) is positive, the absolute value |p-4| can be expressed as (p-4) itself. Rewrite the equation as:
p-4 = 2
Add 4 to both sides of the equation:
p - 4 + 4 = 2 + 4
p = 6
Case 2: (p-4) is negative:
If (p-4) is negative, the absolute value |p-4| is equal to the negation of (p-4), which is -(p-4). Rewrite the equation as:
-(p-4) = 2
Multiply both sides of the equation by -1 to remove the negative sign:
-1 * -(p-4) = 2 * -1
p - 4 = -2
Add 4 to both sides of the equation:
p - 4 + 4 = -2 + 4
p = 2
So, the solutions to the equation 8-3|p-4|=2 are p = 6 and p = 2.