Question

What is the solution of \[2\left( x+4 \right)=12\]?

Answer 1

Hint: We are given a linear equation in a single variable. So firstly, in order to find the value of \[x\], we must perform a monomial to binomial multiplication and then segregate the variables to one side of the equation and constants to the other side. And further solving gives us the solution of the equation.

Complete step-by-step solution:
Now let us know more about the linear equation in a single variable. Generally, the linear equation in a single variable is an equation of a straight line. The general form of a linear equation is \[ax+b=0\], where \[a\ne 0\] and \[a,b\] are real numbers. The linear equation which is a conditional equation will have only one solution. But there are cases in which the system of equations has no solution, unique solution or no solution at all.
Now let us solve the equation \[2\left( x+4 \right)=12\].
Firstly, we will be performing the monomial to binomial multiplication.
We get,
\[\begin{align}
  & 2\left( x+4 \right)=12 \\
 &\Rightarrow 2x+8=12 \\
\end{align}\]
Now we will be transferring the variables to one side and the constants to the other. Then we obtain as follows.
\[2x=12-8\]
On further solving, we get
\[\begin{align}
  & 2x=4 \\
 &\Rightarrow x=2 \\
\end{align}\]
\[\therefore \] The solution of \[2\left( x+4 \right)=12\] is \[2\].

Note: We can also solve the linear equation in one variable by trial and error method. i.e. it would be by substituting a value in the place of variable and checking if the LHS and RHS would be equal or not as shown below. But before substituting the values, we must have a rough idea about the solutions of the equation so that it would not be time consuming and would make it easier in solving.
Now let us substitute \[x=1\] and on solving it, we get
\[\begin{align}
  & 2\left( x+4 \right)=12 \\
 &\Rightarrow 2\left( 1+4 \right)=12 \\
 &\Rightarrow 2\left( 5 \right)=12 \\
 &\Rightarrow 10\ne 12 \\
\end{align}\]
\[\therefore \] \[x=1\] doesn’t satisfy the equation \[2\left( x+4 \right)=12\].
Now let consider \[x=2\] and upon substituting, we get
\[\begin{align}
  & 2\left( x+4 \right)=12 \\
 &\Rightarrow 2\left( 2+4 \right)=12 \\
 &\Rightarrow 2\left( 6 \right)=12 \\
 &\Rightarrow 12=12 \\
\end{align}\]
\[\therefore \] \[x=2\] satisfies the equation \[2\left( x+4 \right)=12\]
Hence \[x=2\] is the solution.