Question

Solve the following equation \[13x - 5 = \dfrac{3}{2}\].

Answer 1

Hint: : Here in this problem we have to find the value of x. As there are no terms involving brackets or parenthesis we have to just concentrate on summing up constant terms. First, in this problem we only have one term consisting of variables and other are constants. We have to combine the constant terms and we have to divide the constant term by the coefficient of x to get the value of x. Finally, we have verified the value of x is correct or not by substituting the value of x in the equation and checking whether L.H.S=R.H.S.

Complete step by step answer:
Given the equation\[13x - 5 = \dfrac{3}{2}\].

\[

13x - 5 = \dfrac{3}{2} \\

\Rightarrow 13x = 5 + \dfrac{3}{2} \\

\Rightarrow 13x = \dfrac{{5 \times 2 + 3}}{2} \\

\Rightarrow 13x = \dfrac{{10 + 3}}{2} \\

\Rightarrow 13x = \dfrac{{13}}{2} \\

\Rightarrow x = \dfrac{{13}}{2} \times \dfrac{1}{{13}} \\

\Rightarrow x = \dfrac{1}{2} \\

\\

\]
Hence the value of x =0.5 or \[\dfrac{1}{2}\].
Verification: We substitute the value of x =\[\dfrac{1}{2}\]in the equation given in question.

\[

13x - 5 = \dfrac{3}{2} \\

\Rightarrow 13 \times \left( {\dfrac{1}{2}} \right) - 5 = \dfrac{3}{2} \\

\Rightarrow \left( {\dfrac{{13}}{2}} \right) - 5 = \dfrac{3}{2} \\

\Rightarrow \dfrac{{13 - 5 \times 2}}{2} = \dfrac{3}{2} \\

\Rightarrow \dfrac{{13 - 10}}{2} = \dfrac{3}{2} \\

\Rightarrow \dfrac{3}{2} = \dfrac{3}{2} \\

\]
Hence it is proved that L.H.S=R.H.S. So we can say that the value of \[x = \dfrac{1}{2}\] for equation\[13x - 5 = \dfrac{3}{2}\].

Note: The above given equation \[13x - 5 = \dfrac{3}{2}\]  is a linear equation in single variable. Solving the equation means getting the value of x. For solving equation like above we have to first simplify terms associated with parenthesis and brackets and then move forward for the variable associated terms. Lastly, we combine constants and then we get the value of variables. 
Checking the terms of left hand side and right hand side assures us with a perfect and accurate answer. As we are solving algebraic expressions and equation, verification (L. H .S = R. H. S) is needed for getting correct answers. This question is a simple algebraic oriented question where no brackets or parenthesis are involved so we can go in a simple way.