Solve each equation. Check your solution.

\[ 14 - 2(3p + 1) = 6(4 + p) \]

Distribute: 14-6p-2=24+6p
Simplify: 12-6p=24+6p -12=12p
Divide by 12: P=-1
Check: 14-2(-3+1)=6(4-1) 14+4=18 18=18

Answered by ohitsjas | 2024-06-10

The solution to the algebraic equation 14 - 2(3p + 1) = 6(4+p) is p = -1. This was determined by expanding both sides, combining like terms, and isolating the variable p. The solution was checked and verified to be correct.

To solve the equation 14 - 2(3p + 1) = 6(4+p), we begin by expanding both sides to eliminate the parentheses.
Expanding the left side: 14 - 2(3p + 1) = 14 - 6p - 2.
Expanding the right side: 6(4 + p) = 24 + 6p.
We then have: 14 - 6p - 2 = 24 + 6p.
Combine like terms and simplify: 12 - 6p = 24 + 6p.
Add 6p to both sides and subtract 12 from both sides: 12 - 6p + 6p - 12 = 24 + 6p + 6p - 12.
This simplifies to: 0 = 24 + 12p - 12.
Further simplification gives us: 0 = 12 + 12p.
Divide by 12 to isolate p: p = -1.
To check the solution, we substitute p = -1 back into the original equation:
14 - 2(3(-1) + 1) = 6(4 - 1).
After simplification, we find that both sides equal 18, confirming that p = -1 is the correct solution.

Answered by NancyJain | 2024-06-24

The solution to the equation 14 − 2 ( 3 p + 1 ) = 6 ( 4 + p ) is p = − 1 . This is verified by substituting p back into the original equation, confirming both sides equal 18. Therefore, the solution checks out correctly.
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Answered by ohitsjas | 2024-12-17