Question

How do you solve \[2\left( 2x+3 \right)-2=5\]?

Answer 1

Hint: Remove the bracket by multiplying the constant (2) with each term inside the bracket. Now, rearrange the terms by leaving the term containing the variable x in the L.H.S. while taking all the constant terms in the R.H.S. Use simple arithmetic operations like: - addition, subtraction, multiplication, division, whichever needed, to make the coefficient of x equal to 1. Accordingly change the R.H.S. to get the answer.

Complete step by step answer:
Here, we have been provided with the linear equation: - \[2\left( 2x+3 \right)-2=5\] and we are asked to solve this equation, that means we have to find the value of x.
Now, removing the bracket by multiplying the constant 2 with each term inside the bracket, we get,
\[\Rightarrow 4x+6-2=5\]
As we can see that the given equation is a linear equation in one variable which is x, so leaving the terms containing the variable x in the L.H.S. and taking all the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 4x=5+2-6 \\
 & \Rightarrow 4x=1 \\
\end{align}\]
Dividing both the sides with 4, we get,
\[\Rightarrow x=\dfrac{1}{4}\]

Hence, the value of x is \[\dfrac{1}{4}\].

Note: One may note that we have been provided with a single equation only. The reason is that we have to find the value of only one variable that is x. So, in general if we have to solve an equation having ‘n’ number of variables then we should be provided with ‘n’ number of equations. Now, one can check the answer by substituting the obtained value of x in the equation provided in the question. We have to determine the value of L.H.S. and R.H.S. separately and if they are equal then our answer is correct.