Answer

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**Hint:**In order to determine the solution of the above linear equation having variable $x$,apply the distributive law to resolve the bracket and then combine all the like terms and transpose the constants terms from LHS to RHS .At the end divide both sides of the equation with the coefficient of variable $x$to get your required result.

**Complete step-by-step solution:**

We are given a linear equation in one variable $x - (12 - x) = 38$. And we have to simplify expression for variable ($x$).Let it be call as $f(x)$

$ \Rightarrow f(x) = x - (12 - x) = 38$

Distributive states that $A(B + C) = A.B + A.C$

By applying the distributive property in order simplify the function, we get

$

x - (12 - x) = 38 \\

x - 12 + x = 38 \\

$

Now we will combine like terms, as you can see we have two terms having variable $x$ in them.so to combine then we actually do the operation with their coefficients and transposing constants from LHS to RHS .

$

2x = 38 + 12 \\

2x = 50 \\

$

Now dividing both sides of the equation with the coefficient of variable $x$,we get

$\dfrac{{2x}}{2} = \dfrac{{50}}{2}$

$x = 25$s

Therefore, the solution of the linear equation $x - (12 - x) = 38$ is $x = 25$.

**Additional Information:**

i) Linear Equation: A linear equation is a equation which can be represented in the form of $ax + c$ where $x$ is the unknown variable and a,c are the numbers known where $a \ne 0$.If $a = 0$ then the equation will become constant value and will no more be a linear equation .

ii) The degree of the variable in the linear equation is of the order 1.

iii) Every Linear equation has 1 root.

**Note:**

1. One must be careful while calculating the answer as calculation error may come.

2.Distributive proper is also known as the distributive law of multiplication or division.

3. We use the distributive property generally when the two terms inside the parentheses cannot be added or operated because they are not the like terms.

4.We always have to ensure that the outside number is applied to all the terms inside the parentheses.

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