Question

How do you solve \[2\left( {x - 4} \right) = 12\]

Answer 1

Hint: We have given an expression in one variable, and we need to solve this for \['x'\] .We will solve it, first by opening the parenthesis. Then we will solve this using the transposition method. The common transposition method is to do the same calculation (mathematically) on both sides of the equation, with the aim of bringing like terms together and isolating the variable terms. That is, we group the \['x'\] components on one side of the equality and the constant terms on the other side and solve the resultant expression to get the value of \['x'\]

Complete step-by-step answer:
In this question we have given an expression i.e., \[2\left( {x - 4} \right) = 12{\text{ }} - - - \left( 1 \right)\]
And we have to find the value of \['x'\]
Firstly, we will open up the parenthesis in the given expression
Therefore, equation \[\left( 1 \right)\] becomes,
\[2x - 8 = 12\]
Now, we transpose \[8\] which is present in the left-hand side of the equation to the right side of the equation by adding \[8\] on the right side of the equation.
Therefore, we get
\[2x = 12 + 8\]
On adding the terms on the right-hand side, we get
\[2x = 20\]
Now we transpose \[2\] which is present in the left-hand side of the equation to the right-hand side of the equation by dividing \[2\] on the right-hand side of the equation,
Therefore, we get
\[x = \dfrac{{20}}{2}\]
On dividing the terms on the right-hand side, we get
\[x = 10\]
which is the required answer.
So, the correct answer is “\[x = 10\]”.

Note: In mathematics, to solve an equation means to find its solution, which satisfies the given conditions stated by the given expression. We can also check whether the obtained result is correct or not. All we need to do is just substitute the value of \['x'\] in the given expression.
Like the given expression is, \[2\left( {x - 4} \right) = 12\]
On substituting \[x = 10\] we get,
\[2\left( {10 - 4} \right) = 12\]
\[ \Rightarrow 2\left( 6 \right) = 12\]
On multiplying, we get
\[ \Rightarrow 12 = 12\]
Thus, left-hand side is equals to right-hand side