Q31. - Algebra 1

Question

Solve each equation. Check your solution.

$45=7-5\mathrm{n}$

Step-by-Step Solution

Answer

The solution of the given equation is $n=-\frac{38}{5}$.

Step 1. Write the given equation.

The given equation is “$45=7-5n$”.

Step 2. Solve the given equation.

Solving,

 

$45=7-5n$  (Given equation)

 

$45-7=7-5n-7$  (Subtract 7 from both sides)

 

$38=-5n$  (Simplify)

 

$\frac{38}{-5}=\frac{-5n}{-5}$  (Divide both sides by $-5$)

 

$-\frac{38}{5}=n$  (Simplify)

 

$n=-\frac{38}{5}$  (Write the variable on the left-hand side)

 

So, $n=-\frac{38}{5}$ is the solution of the given equation.

Step 3. Check the obtained solution.

Put $n=-\frac{38}{5}$ in the given equation $45=7-5n$ to get,

 

$\begin{array}{l}45=7-5\left(-\frac{38}{5}\right)\\ 45=7-1\left(-38\right)\\ 45=7+38\\ 45=45\end{array}$

 

Since the value obtained on the left-hand side and right-hand side are equal, the obtained value is indeed a solution of the given equation.