Question

How do you solve $2-15n=5\left( -3n+2 \right)$

Answer 1

Hint: To solve the given equation first we solve the parenthesis given in the equation. For this we will multiply the terms inside the bracket by 5 on the RHS. Then we will shift the constant terms to the RHS and keep variable terms at the LHS. Then we solve the equation by solving the algebraic operations like subtraction, addition, multiplication and division.

Complete step by step solution:
We have been given an equation $2-15n=5\left( -3n+2 \right)$.
We have to find the value of n by solving the given equation.
The given equation is $2-15n=5\left( -3n+2 \right)$
Let us first solve the parenthesis given in the equation. For this we multiply the terms inside the bracket by 5. Then we will get
$\Rightarrow 2-15n=-15n+10$
Now, shifting the constant terms to the right side of the equation and keeping the variable terms to the left side of the equation we will get
$\Rightarrow -15n+15n=10-2$
Now, solving the above obtained equation we will get
$\begin{align}
  & \Rightarrow 0=10-2 \\
 & \Rightarrow 10=2 \\
\end{align}$
The above obtained equation is not a valid statement. As we have to find the value of variable and variable disappears from the equation. It means the equation has no solution.

Note:
A linear equation has no solution means the equation cannot be true for any value we assign to the variable. An equation sometimes has infinite solutions means the equation is true for any value we assign to the variable. Generally a linear equation in one variable has only one unknown variable and has only one solution.