Solving an equation means finding a value of a variable that make the equation true. This value is called the solution of the equation. A mathematical equation is just like a balanced equation. Both sides of the equation should be equal at all times. Whatever we do to one side, has to be done on the opposite side.
\(9|4p + 2| + 8 = 35\)
\(9|4p+2|=35-8\) \(Subtract \ 8 \ from \ both \ sides\)
\(9|4p+2|=27\)
\(|4p+2|= \dfrac{27}{9}\) \(Divide \ both \ sides \ by \ 9\)
\(|4p+2|=3\)
\(Break \ down \ the \ problem \ into \ these \ 2 \ equations\)
\(4p+2=3\)
\(-(4p+2)=3\)
\(Solve \ the \ 1st \ equation: \ 4p+2=3\)
\(4p=3-2\) \(Subtract \ 2 \ from \ both \ sides\)
\(4p=1\)
\(p= \dfrac{1}{4}\) \(Divide \ both \ sides \ by \ 4\)
\(Solve \ the \ 2nd \ equation: \ -(4p+2)=3\)
\(-4p−2=3\) \(Simplify \ brackets\)
\(-4p=3+2\) \(Add \ 2 \ to \ both \ sides\)
\(-4p=5\)
\(p= -\dfrac{5}{4}\)
\(Collect \ all \ solutions\)
\(p= -\dfrac{5}{4}\) , \(p= \dfrac{1}{4}\)