Question

Find and correct the errors in the mathematical statement $\frac{7x+5}{5}=7x$

Answer 1

Find and correct errors in the given statement:

An equation is a mathematical expression of equality between two algebraic expressions that have equal values.

Given, $\frac{7x+5}{5}=7x$

On simplifying L.H.S, we get,

$$\begin{gathered} =\frac{7x+5}{5} \\ =\frac{7x}{5}+\frac{5}{5} \\ =\frac{7x}{5}+1 \end{gathered}$$

But, it is given that R.H.S $=7x$

Thus, L.H .S.$\ne$ R.H.S.

So,for correct statement we need to replace $7x$ with $1+\frac{7x}{5}$in RHS.

Hence, the correct statement is $\frac{\mathbf{7}\mathbf{x}\mathbf{+}\mathbf{5}}{\mathbf{5}}\mathbf{=}\mathbf{}\frac{\mathbf{7}\mathbf{x}}{\mathbf{5}}\mathbf{+}\mathbf{1}$.