Question

Solve and find value of x: \[\dfrac{{x - 2}}{3} - \dfrac{{x + 3}}{7} = \dfrac{3}{8}\]

Answer 1

Hint: These are equations with one or single variable . We get a single value of that variable after solving it. First we will take the LCM of denominators on LHS terms. Then we will take the x terms on one side and constant terms on the other side. This will help us in calculating the value of x.

Complete step-by-step answer:
Given that,
\[\dfrac{{x - 2}}{3} - \dfrac{{x + 3}}{7} = \dfrac{3}{8}\]
Taking LCM on LHS,
\[
   \Rightarrow \dfrac{{7\left( {x - 2} \right) - 3\left( {x + 3} \right)}}{{3 \times 7}} = \dfrac{3}{8} \\
   \Rightarrow \dfrac{{7x - 14 - 3x - 9}}{{21}} = \dfrac{3}{8} \\
\]
Taking x terms on one side,
\[
   \Rightarrow \dfrac{{7x - 3x - 14 - 9}}{{21}} = \dfrac{3}{8} \\
   \Rightarrow \dfrac{{4x - 23}}{{21}} = \dfrac{3}{8} \\
   \Rightarrow 4x - 23 = \dfrac{3}{8} \times 21 \\
\]
Now taking 23 on RHS and 4x on LHS
\[
   \Rightarrow 4x = \dfrac{{63}}{8} + 23 \\
   \Rightarrow 4x = 7.875 + 23 \\
   \Rightarrow 4x = 30.875 \\
\]
Now in last step we will find the value of x
\[
   \Rightarrow x = \dfrac{{30.875}}{4} \\
   \Rightarrow x = 7.7187 \\
\]
Value of x is 7.7187.

Note: Don’t directly add or subtract the ratios. Finding LCM is the basic step in these types of problems. Then only proceed to solve. LCM is nothing but the cross multiplication