Answer: The required value of p is \(-\dfrac{150}{23}.\)
Step-by-step explanation: We are given to solve the following linear equation for p :
\(p-160=22+8(3p-4)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
To solve the given equation for p, we must bring all the terms involving p on the left hand side and the other constant terms on the right hand side of the equation.
The solution of equation (i) is as follows :
\(p-160=22+8(3p-4)\\\\\Rightarrow p-160=22+24p-32\\\\\Rightarrow p-160=24p-10\\\\\Rightarrow 24p-p=-160+10\\\\\Rightarrow 23p=-150\\\\\Rightarrow p=-\dfrac{150}{23}.\)
Thus, the required value of p is \(-\dfrac{150}{23}.\)
