Question

Solve: $0.4\left( 3x-1 \right)=0.5x+1$ .

Answer 1

Hint: We have been given linear equations in one variable and we need to find a solution to this equation. We will use the collection method to solve our problem. In this method, all the variable terms are written on one side of the equation whereas all the constant terms are written on another side of the equation. This gives us an equation in a single variable, thus giving us a solution. We shall proceed like this to get our answer.

Complete step-by-step answer:
The linear equation given to us in the problem is equal to:
$\Rightarrow 0.4\left( 3x-1 \right)=0.5x+1$
In the above expression, let us first of all re-write the decimal terms in their fractional form. This can be done by dividing each successive digit after decimal by 10. This will make the calculations easier to analyze and solve. On doing so, we get the new expression as:
$\Rightarrow \dfrac{4}{10}\left( 3x-1 \right)=\dfrac{5}{10}x+1$
On simplifying the fractions into their lowest terms, we get the resulting expression as:
$\Rightarrow \dfrac{2}{5}\left( 3x-1 \right)=\dfrac{x}{2}+1$
Now, we can proceed in solving our equation as follows:
$\Rightarrow \dfrac{6x}{5}-\dfrac{2}{5}=\dfrac{x}{2}+1$
Collecting all the variable terms in the left-hand side of our equation and all the constant terms on the right-hand side of our expression, we get:
$\begin{align}
  & \Rightarrow \dfrac{6x}{5}-\dfrac{x}{2}=\dfrac{2}{5}+1 \\
 & \Rightarrow \dfrac{12x-5x}{10}=\dfrac{2+5}{5} \\
 & \Rightarrow \dfrac{7x}{10}=\dfrac{7}{5} \\
 & \Rightarrow x=2 \\
\end{align}$
Hence, on solving the linear equation $0.4\left( 3x-1 \right)=0.5x+1$, we get the unique result in ‘x’ as 2. Hence, $x=2$ is the solution to our problem.

Note: Whenever solving a problem containing linear equations, we should always verify our answer by putting the solution in the original expression. Here, if we put $x=2$, in our original expression, then we get the left-hand value of our expression as: $0.4\left( 3\times 2-1 \right)=2$ and the right-hand value as: $0.5\times 2+1=2$. Since, $L.H.S.=R.H.S.$, our answer is correct and verified.