Question

Solve the given expression:
\[\dfrac{a-8}{3}=\dfrac{a-3}{2}\]

Answer 1

Hint: For the given expression, apply cross multiplication properly. Simplify the expression formed by using arithmetic operations and find the value of a.

Complete step-by-step answer:
We have been given an expression with one variable as ‘a’. We need to solve the given expression and find the value of a.
We have been given the expression,
\[\dfrac{a-8}{3}=\dfrac{a-3}{2}\]
Let us apply the cross multiplication property on the above expression,
\[\Rightarrow 2\left( a-8 \right)=3\left( a-3 \right)\]
Now, let us open the brackets and apply the arithmetic operation of multiplication.
\[\begin{align}
  & \Rightarrow 2\left( a-8 \right)=3\left( a-3 \right) \\
 & \Rightarrow 2a-\left( 2\times 8 \right)=3a-\left( 3\times 3 \right) \\
\end{align}\]
\[\Rightarrow \]\[2a-16=3a-9\], let us rearrange the expression.
\[\begin{align}
  & \Rightarrow 3a-2a=-16+9 \\
 & \Rightarrow a=-16+9=-7 \\
\end{align}\]
Hence we got the value of a as (-7).
Thus we can verify the same by putting a = -7 in the given expression.
Put a = -7 in the LHS of the expression,
LHS = \[\dfrac{a-8}{3}=\dfrac{-7-8}{3}=\dfrac{-15}{3}=-5\]
\[\therefore \] LHS = -5
Similarly, let us put a = -7 in the RHS of the given expression,
RHS = \[\dfrac{a-3}{2}=\dfrac{-7-3}{2}=\dfrac{-10}{2}=-5\]
\[\therefore \] RHS = -5
Thus we got LHS = RHS = -5
\[\therefore \] a = -7 is the solution of the given expression.

Note: You can also split the expression and solve without using cross multiplication property. You can split it as,
\[\begin{align}
  & \Rightarrow \dfrac{a}{3}-\dfrac{8}{3}=\dfrac{a}{2}-\dfrac{3}{2}\Rightarrow \dfrac{a}{3}-\dfrac{a}{2}=\dfrac{8}{3}-\dfrac{3}{2} \\
 & \Rightarrow \dfrac{2a-3a}{6}=\dfrac{16-9}{6}\Rightarrow 2a-3a=16-8 \\
 & \therefore a=-7 \\
\end{align}\]