Question

Describe and correct the error in solving the following equation:$-2(5-n)=2$

Short answer

The correct solution will be,

$\begin{array}{c}-2(5-n)=2\\ -10+2n=2\\ -10+2n+10=2+10\\ 2n=12\\ n=6\end{array}$

Step-by-step solution

– Given information.

The given equation is:$-2(5-n)=2$

– Write the incorrect solution.

The incorrect solution is:

$\begin{array}{c}-2(5-n)=2\\ -10-2n=2\\ -10-2n+10=2+10\\ -2n=12\\ n=-6\end{array}$

– Describe the correct solution.

The error in solving the equation is in the first step where distributive property is used,

$-10-2n=2$

Here, when –2 is multiplied with –n, the sign of the product changes since, they have the same sign (negative).

Hence, the correct solution will be,

$\begin{array}{c}-2(5-n)=2\\ -10+2n=2\\ -10+2n+10=2+10\\ 2n=12\\ n=6\end{array}$