Question

Solve the linear equation below and find the value of p:
$\dfrac{3p+2}{2}+7=17.$

Answer 1

Hint: The equation given in question as a linear equation is one variable which can be solved by putting all the variable terms in one side and constant terms on the other side. For this, we will do the addition or subtraction of constants and cross multiplication of constants wherever required.

Complete step-by-step answer:
Before solving the question, we must know what is a linear equation in one variable. The linear equation is one variable is an equation which is expressed in the form of $ax+b=0$, where a and b are two integers and x is variable and has only one solution. The linear equation is one variable that can be solved by putting all the variable terms on one side of the equation. The equation given in the question is: $\dfrac{3p+2}{2}+7=17.$
Now, to solve constants and variables, we will first subtract 7 from both sides of the equation. After doing this, we will get:
$\begin{align}
  & \Rightarrow \dfrac{3p+2}{2}+7-7=17-7 \\
 & \Rightarrow \dfrac{3p+2}{2}+0=10 \\
 & \Rightarrow \dfrac{3p+2}{2}=10 \\
\end{align}$
Now, we will cross multiply 2 from LHS to RHS. After doing this, we will get the following equation:
$\begin{align}
  & \Rightarrow 3p+2=10\times 2 \\
 & \Rightarrow 3p+2=20 \\
\end{align}$
Now, we will subtract 2 from both sides of the equation. After doing this, we will get:
$\begin{align}
  & \Rightarrow 3p+2-2=20-2 \\
 & \Rightarrow 3p+0=18 \\
 & \Rightarrow 3p=18 \\
\end{align}$
Now, we will divide the whole equation by 3. After dividing, we will get:
$\begin{align}
  & \Rightarrow \dfrac{3p}{3}=\dfrac{18}{3} \\
 & \Rightarrow p=6 \\
\end{align}$
Thus, the value of p=6.

Note: The above linear equation is one variable that can be solved alternatively by the following method. First, we will take LCM on the left hand side, thus we will get:
$\begin{align}
  & \dfrac{3p+2+2\left( 7 \right)}{2}=17 \\
 & \Rightarrow \dfrac{3p+2+14}{2}=17\Rightarrow \dfrac{3p+16}{2}=17 \\
\end{align}$
Now, we will cross multiply 2$\Rightarrow 3p+16=34.$ Now, we will subtract 16 from both sides of the question. Thus: $3p=34-16\Rightarrow 3p=18\Rightarrow p=\dfrac{18}{3}\Rightarrow p=6$.