Question

Solve $\dfrac{2}{3}x + 1 = \dfrac{1}{2}x$.

Answer 1

Hint: In this question we have to solve the equation for \[x\], the given equation is a linear equation as the degree of the highest exponent of \[x\] is equal to 1. To solve the equation take all \[x\] terms to one side and all constants to the other side and solve for required \[x\].

Complete step-by-step answer:
Given equation is $\dfrac{2}{3}x + 1 = \dfrac{1}{2}x$, and we have to solve for \[x\],
Given equation is a linear equation as the highest degree of \[x\] will be equal to 1,
Now transform the equation by taking all \[x\] terms to one side and all constants to the other side we get,
\[ \Rightarrow \dfrac{2}{3}x + 1 = \dfrac{1}{2}x\],
Now transforming the equation by taking all \[x\] terms to one side and all constant terms to one side we get,
\[ \Rightarrow \dfrac{2}{3}x - \dfrac{1}{2}x = - 1\],
Now taking L.C.M on the left hand side we get,
\[ \Rightarrow x = - 6\] \[ \Rightarrow \dfrac{{2 \times 2}}{{3 \times 2}}x - \dfrac{{1 \times 3}}{{2 \times 3}}x = - 1\],
Now simplifying we get,
\[ \Rightarrow \dfrac{4}{6}x - \dfrac{3}{6}x = - 1\],
As the denominators are equal we can subtract we get,
\[ \Rightarrow \dfrac{{4x - 3x}}{6} = - 1\],
Now simplifying we get,
\[ \Rightarrow \dfrac{x}{6} = - 1\],
Now multiplying 6 to both sides we get,
\[ \Rightarrow \dfrac{x}{6} \times 6 = - 1 \times 6\],
Now simplifying we get,
\[ \Rightarrow x = - 6\],
So the value of \[x\] will be -6, i.e., when we substitute the value of \[x\] in the equation $\dfrac{2}{3}x + 1 = \dfrac{1}{2}x$, then right hand side of the equation will be equal to left hand side of the equation, we get,
\[ \Rightarrow \dfrac{2}{3}x + 1 = \dfrac{1}{2}x\],
Now substitute \[x = - 6\], we get,
\[ \Rightarrow \dfrac{2}{3}\left( { - 6} \right) + 1 = \dfrac{1}{2}\left( { - 6} \right)\],
Now simplifying we get,
\[ \Rightarrow 2\left( { - 2} \right) + 1 = - 3\],
Now simplifying by adding we get,
\[ \Rightarrow - 4 + 1 = - 3\],
Further simplifying we get,
\[ \Rightarrow - 3 = - 3\],
So R.H.S=L.H.S.

\[\therefore \]The value of \[x\] when the equation $\dfrac{2}{3}x + 1 = \dfrac{1}{2}x$ is solved will be equal to -6.

Note:
A linear equation is an equation of a straight line having a maximum of one variable. The degree of the variable will be equal to 1. To solve any equation in one variable, pit all the variable terms on the left hand side and all the numerical values on the right hand side to make the calculation solved easily.