Let's solve the equation step by step.
Starting with the given equation:
–6p + 7 = 3(2p – 3) – 4(–10 + 4p)
First, simplify the expressions inside the parentheses:
–6p + 7 = 3(2p – 3) + 4(10 - 4p)
Next, distribute the coefficients to the terms inside the parentheses:
–6p + 7 = 6p - 9 + 40 - 16p
Combine like terms:
–6p + 7 = -10p + 31
Now, isolate the variable term by moving the constant term to the other side:
–6p + 10p = 31 - 7
4p = 24
Finally, solve for p by dividing both sides by 4:
p = 24/4
p = 6
So, the solution to the equation is p = 6.