Question

Solve the linear equation $5\left( x+4 \right)+8=68$ for the value of x and check the result.

Answer 1

Hint: Here, we will first of all take the terms containing x to one side of the equation and the constant terms to the other side. And after that we can easily get the value of x.

Complete step-by-step answer:

We know that a linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form $ax+b=0$, where x is the variable, ‘a’ and ‘b’ are real numbers and are not equal to zero.
 The steps for solving a linear equation in one variable are as follows:
In the first step, transfer all the variables on one side of the equation, that is transfer variables on one side of the equation and constants on the other side.
Then in the next step we get the value of the variable by solving.
Here, the equation given to us is:
$5\left( x+4 \right)+8=68$
 On subtracting 8 from both sides of the equation, we get:
$\begin{align}
  & 5\left( x+4 \right)+8-8=68-8 \\
 & \Rightarrow 5x+20=60 \\
\end{align}$
On subtracting 20 from both sides of the equation, we get:
$\begin{align}
  & 5x+20-20=60-20 \\
 & \Rightarrow 5x=40 \\
\end{align}$
On dividing both sides of the equation by 5, we get;
$\begin{align}
  & \dfrac{5x}{5}=\dfrac{40}{5} \\
 & \Rightarrow x=8 \\
\end{align}$
So, the value of x comes out to be 8.
Hence, the solution of the given linear equation is x = 8.
Now, to check our result, we will put the value x = 8 in the LHS of the given equation and check whether its value is equal to the RHS or not.
So, on putting x = 8 in LHS, we get:
$LHS=5\left( 8+4 \right)+8=5\times 12+8=60+8=68$
Since, the RHS is also equal to 68.
So, we have LHS = RHS.
Hence, x = 8 is the correct solution of the given linear equation.

Note: Students should note here that we can directly transfer a term from one side of the equation to the other side but it should be kept in mind that the sign of the term gets reversed when it is transferred from one side to another.