Question

Algebra Basics Solve the equation. Check your solution. (Lesson 2.5)

$\mathbf{b}\mathbf{+}\mathbf{14}\mathbf{=}\mathbf{91}$

Short answer

The solution for the equation $b+14=91$ is $b=77$.

Step-by-step solution

.  Separate the variable and constants

Write the original equation and separate the variables.

$\begin{array}{l}b+14=91\text{}\left[\text{Writeoriginalequation.}\right]\text{}\\ b+14-14=91-14\text{}\left[\text{Subtract14fromeachside.}\right]\text{}\end{array}$

.  Simplify both sides

Simplify the equation on both sides to solve it.

$\begin{array}{l}b=91-14\\ b=77\end{array}$

Therefore, the solution of the equation is $b=77$.

.  Check the solution 

To check the solution, write the original equation and substitute the value of b.

$b+14=91$

Now, substitute$b=77$and check the result.

$\begin{array}{l}b+14=91\text{}\left[\text{Writeoriginalequation.}\right]\text{}\\ 77+14=91\text{}\left[\text{Substitute77forb.}\right]\text{}\\ 91=91\end{array}$

As the left-hand side is equal to right hand side, this signifies that the solution is correct.