Question

Solve the equation and graph the solution(s), if possible. 9|4p + 2| + 8 = 35

Answer 1

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.

$9|4p + 2| + 8 = 35$ 

$9|4p+2|=35-8$                $Subtract \ 8 \ from \ both \ sides$
 
$9|4p+2|=27$ 

$|4p+2|= \dfrac{27}{9}$    $Divide \ both \ sides \ by \ 9$

$|4p+2|=3$ 

$Break \ down \ the \ problem \ into \ these \ 2 \ equations$ 

$4p+2=3$ 

$-(4p+2)=3$ 

$Solve \ the \ 1st \ equation: \ 4p+2=3$ 

$4p=3-2$    $Subtract \ 2 \ from \ both \ sides$ 

$4p=1$ 

$p= \dfrac{1}{4}$    $Divide \ both \ sides \ by \ 4$ 

$Solve \ the \ 2nd \ equation: \ -(4p+2)=3$ 

$-4p−2=3$   $Simplify \ brackets$ 

$-4p=3+2$       $Add \ 2 \ to \ both \ sides$ 

$-4p=5$ 

$p= -\dfrac{5}{4}$ 

$Collect \ all \ solutions$ 

$p= -\dfrac{5}{4}$ , $p= \dfrac{1}{4}$