Q27. - Algebra 2

Question

Solve the equation and check the solution.

$7+5n=-58$

Step-by-Step Solution

Answer

The solution is $n=-13$.

Step 1- Consider the equation.

Consider the equation $7+5n=-58$.

Add 58 on both sides of the equation.

Step 2- Step description.

$\begin{array}{l}7+5n=-58\\ 7+5n+58=-58+58\\ 7+5n+58=0\\ 5n+65=0\end{array}$

Step 3- Step description.

Subtract $-65$ from both sides of the equation as follows:

 $\begin{array}{l}5n+65=0\\ 5n+65-65=-65\\ 5n=-65\end{array}$ 

Divide both sides of the equation by 5

$\begin{array}{l}5n=-65\\ n=-\frac{65}{5}\\ n=-13\end{array}$

Therefore, the solution is $n=-13$.

Step 4- Verify the solution.

Substitute $n=-13$ in the equation and simplify as follows:

 $\begin{array}{l}7+5n=-58\\ 7+5\left(-13\right)=-58\\ 7-65=-58\\ -58=-58\end{array}$

Since the left-hand side of the equation is equal to the right-hand side of the equation, therefore, the solution is $n=-13$.