Question

Solve each equation. Check your solution.

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

Short answer

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

Step-by-step solution

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)

role="math" localid="1642484583779" $45-7=7-5n-7$ (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.