Question

Solve the following:
\[\dfrac{{3x}}{4} - \dfrac{1}{4}\left( {x - 20} \right) = \dfrac{x}{4} + 32\]
\[A.112 \]
\[B.126 \]
\[C.108 \]
\[D.102 \]

Answer 1

Hint: In this type of question a linear equation is given and we have to solve the equation and then find the value of \[x\], we will find the value of \[x\] by putting the same terms containing \[x\] on both sides and constants terms on other side and then we will solve them so that we could obtain the desired value of \[x\] after that we will the check result by putting the value of\[x\] on both sides of the equation and if Left-hand side is equal to right hand side then the required value obtained is true.

Complete answer:
An algebraic equation is made up of variables, constants and coefficients .The coefficients are the numbers related with the variables, while the constants are also independent numbers in the equation. The algebraic equations are having different orders, orders are the highest powers of variables, if highest power of variable is one then they is known as linear equations. Linear equations are first-order equations. In the coordinate system, these equations are defined for lines. A linear equation is an equation for a straight line.
Finding the value of a variable for which the equation becomes true is known as the solution of the equation. For each variable in a linear equation, there is usually only one solution. For equation of two variables we have two solutions and so on.
There are different types of equation can be possible: -
1. Linear equations are linear equations that have only one variable and having highest degree as one.
2. Quadratic equations having one variable but highest degree of variable are two.
3. Cubic equation having one variable but highest degree of variable is three.
Now according to the given question:
We have given the linear equation as
\[\dfrac{{3x}}{4} - \dfrac{1}{4}\left( {x - 20} \right) = \dfrac{x}{4} + 32\]
Multiply all terms and we will get,
\[ \Rightarrow \dfrac{{3x}}{4} - \dfrac{x}{4} + \dfrac{{20}}{4} = \dfrac{x}{4} + 32\]
On Solving we get,
\[ \Rightarrow \dfrac{{3x}}{4} - \dfrac{x}{4} + 5 = \dfrac{x}{4} + 32\]
Rearrange the terms, put the terms of \[x\] on one side and constant on other side then we will get,
\[ \Rightarrow \dfrac{{3x}}{4} - \dfrac{x}{4} - \dfrac{x}{4} = 32 - 5\]
Take the LCM on left hand side we get,
\[ \Rightarrow \dfrac{{3x - x - x}}{4} = 27\]
\[ \Rightarrow \dfrac{{3x - 2x}}{4} = 27\]
\[ \Rightarrow \dfrac{x}{4} = 27\]
\[ \Rightarrow x = 27 \times 4\]
\[\therefore x = 108\]
The value of the given equation after solving is \[108\]

Hence option \[(C)\] is correct as the value of \[x\] is \[108\]

Note:
Algebraic linear equations basically of two type’s linear equation or linear inequation, In linear equation only equality symbol is used while inequation consists of all sign rather only equality symbol. All straight lines follow linear equation. A straight line is not obtained by a non-linear equation.