Question

Solve the following equation and check your results: $x=\frac{4}{5}\left(x+10\right)$

Answer 1

Step 1. Solution of the given equation

Solve the given equation by Rearranging and combining the like terms:

$\begin{array}{l}x=\frac{4}{5}\left(x+10\right)\\ \Rightarrow 5x=4\left(x+10\right)\\ \Rightarrow 5x=4x+40\\ \Rightarrow 5x-4x=40\\ \Rightarrow x=40\end{array}$

Step 2. Verification

Verify the result by substituting $x=40$ in the given equation:

$$\begin{gathered} \mathrm{LHS}=x \\ =40 \\ \mathrm{And}, \\ \begin{array}{l}\mathrm{RHS}=\frac{4}{5}\left(x+10\right)\\ =\frac{4}{5}\left(40+10\right)\\ =\frac{4}{5}\left(40+10\right)\\ =\frac{4}{5}\times 50\\ =40\end{array} \end{gathered}$$

$\because \mathrm{LHS}=\mathrm{RHS}$

Hence, the solution of $x=\frac{4}{5}\left(x+10\right)$ is $x=40$ and it is verified.