# Solve the following equation and check your result:

\[2x - 1 = 14 - x\]

Answer

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Hint:- Take constant terms and variables from different sides of the equation.

As, we are given the equation,

\[ \Rightarrow 2x - 1 = 14 - x\] (1)

As, we can see from the above equation that the given equation has only one variable.

So, whenever we are given with one equation having one variable then we will find the

value of variable by taking all the constant terms to one side of the equation.

And variable to the other side of the equation.

So, now for solving equation 1.

Adding \[x + 1\] to both sides of the equation 1. We get,

\[ \Rightarrow 3x = 15\]

Now, dividing both sides of the above equation by 3. We get,

\[ \Rightarrow x = \dfrac{{15}}{3} = 5\].

For checking the result.

If LHS = RHS, On putting the value of $x$ in the given equation. Then our result will be satisfied.

Putting the value of $x$ in equation 1.

\[

\Rightarrow (2*5) - 1 = 14 - 5 \\

\Rightarrow 9 = 9 \\

\]

Hence, LHS = RHS

So, the value of $x$ will be 5.

Note:- In these types of questions if there are n variables in an equation then there should be

minimum of n different equations, to get the value of all variables. And easiest and efficient

way to get values of different variables is by substituting the values of variables in different

equations.

As, we are given the equation,

\[ \Rightarrow 2x - 1 = 14 - x\] (1)

As, we can see from the above equation that the given equation has only one variable.

So, whenever we are given with one equation having one variable then we will find the

value of variable by taking all the constant terms to one side of the equation.

And variable to the other side of the equation.

So, now for solving equation 1.

Adding \[x + 1\] to both sides of the equation 1. We get,

\[ \Rightarrow 3x = 15\]

Now, dividing both sides of the above equation by 3. We get,

\[ \Rightarrow x = \dfrac{{15}}{3} = 5\].

For checking the result.

If LHS = RHS, On putting the value of $x$ in the given equation. Then our result will be satisfied.

Putting the value of $x$ in equation 1.

\[

\Rightarrow (2*5) - 1 = 14 - 5 \\

\Rightarrow 9 = 9 \\

\]

Hence, LHS = RHS

So, the value of $x$ will be 5.

Note:- In these types of questions if there are n variables in an equation then there should be

minimum of n different equations, to get the value of all variables. And easiest and efficient

way to get values of different variables is by substituting the values of variables in different

equations.

Last updated date: 17th Sep 2023

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