Final answer:
To solve the equation -3p+7=6-(8p+8), distribute the negative sign, combine like terms, and solve for p. The solution is p = -9/5 or -1.8, which can be checked by substituting it back into the original equation.
Step-by-step explanation:
To solve the equation -3p+7=6-(8p+8), we need to simplify both sides of the equation and then solve for p. Distributing the negative sign to the terms inside the parentheses on the right side of the equation: -3p + 7 = 6 - 8p - 8. Combining like terms: -3p + 7 = -8p - 2. Adding 8p to both sides: 5p + 7 = -2. Subtracting 7 from both sides: 5p = -9. Dividing both sides by 5: p = -9/5 or -1.8.
To check the solution, substitute p = -9/5 or -1.8 back into the original equation: -3(-9/5) + 7 = 6 - (8(-9/5) + 8). After simplifying, we get -27/5 + 7 = 6 - (-72/5 + 8), which becomes -27/5 + 7 = 6 + 72/5 - 8. Continuing, -27/5 + 7 = 60/5 + 72/5 - 40/5, which simplifies to -27/5 + 7 = 92/5 - 40/5. Finally, -27/5 + 7 = 52/5, which is a true statement. Therefore, the solution p = -9/5 or -1.8 is correct.
Learn more about Solving linear equations with distribution and simplifying