Question

How do you solve \[\dfrac{2}{3}x = \dfrac{3}{8}x + \dfrac{7}{{12}}\]?

Answer 1

Hint: This is a linear equation with a single variable. Solving this equation means to find the value of the variable present in the equation. To solve it, we will shift the term containing the variable from RHS to LHS. Then we will subtract them and then solve the resulting equation to get the value of the variable.

Complete step by step answer:
We have;
\[\dfrac{2}{3}x = \dfrac{3}{8}x + \dfrac{7}{{12}}\]
Now shifting the first term of the RHS to LHS we get;
\[ \Rightarrow \dfrac{2}{3}x - \dfrac{3}{8}x = \dfrac{7}{{12}}\]
Now we will take \[x\] common in the LHS. So, we get;
\[ \Rightarrow \left( {\dfrac{2}{3} - \dfrac{3}{8}} \right)x = \dfrac{7}{{12}}\]
Now we will take the LCM and simplify the fraction in the LHS. So, we get;
\[ \Rightarrow \left( {\dfrac{{16 - 9}}{{24}}} \right)x = \dfrac{7}{{12}}\]
On simplification, we get;
\[ \Rightarrow \left( {\dfrac{7}{{24}}} \right)x = \dfrac{7}{{12}}\]
Now we cancel \[7\] from the numerators of both sides. So, we get;
\[ \Rightarrow \left( {\dfrac{1}{{24}}} \right)x = \dfrac{1}{{12}}\]
Now we will cross multiply \[24\]. So, we have;
\[ \Rightarrow x = \dfrac{{24}}{{12}}\]
On dividing we get;
\[ \Rightarrow x = 2\]

Note:
A linear equation has only one root i.e. There is only one value of \[x\] for which the equation gets satisfied. So, when we draw the graph of a linear equation it cuts the \[x\]-axis only once. Also, the graph of a linear equation is a straight line. Suppose we have a linear equation with the equation given above as \[y = \dfrac{7}{{24}}x - \dfrac{7}{{12}}\]. If we draw its graph it will look like a straight line and since we have got the value of \[x = 2\] so, it will cut the x-axis at only one point and that point will be \[x = 2\]. Also, if we calculate the slope of this line, we will find it to be \[\dfrac{7}{{24}}\].