Solve: 42 = -8(7+4p)+2
Answer
p = -3
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Step-by-Step Breakdown
- Expand and simplify the left-hand side: 42 = 42
- Expand and simplify the right-hand side: -8(7+4p)+2 = -32p - 54
- Move every term to one side so the equation reads "...= 0": 32p + 96 = 0
- This is a linear equation of the form ap+b=0, with a=32 and b=96.
- Solve for p: p = -b/a = -(96)/32 = -3
Theory & Definitions
A linear equation in one unknown can always be rearranged into the form ap+b=0 (a≠0), which has exactly one solution: p = -b/a.
Frequently Asked Questions
What is the solution to 42 = -8(7+4p)+2?
p = -3.