Question

Solve each equation. Check your solution. (Lesson 2-2). (p. 110)

$-26=b-3$

Short answer

The solution of the equation is $b=-23$.

Step-by-step solution

Step 1. Apply the concept of addition and subtraction of equality.

An equation is an expression containing two quantities separated by a $=$symbol.

Finding solution to an equation involves separating the variable on one side of the equation and numbers on the other side.

We can add or subtract same quantities on both sides of the equation for separating the variable on one side of the equation and the numbers on the other side.

For example, in the equation below we add 5 from both sides of the equation to find a solution:

$\begin{array}{l}x-5=10\\ x-5+5=10+5\end{array}$

We are given the equation $-26=b-3$, we add 3 from both sides of the equation as shown:

$-26+3=b-3+3$

Step-2. Simplify the expression.

We subtracted 8 from both sides of the equation and obtained:

$-26+3=b-3+3$

Next we simplify the expression as shown:

$\begin{array}{l}-26+3=b-3+3\\ -23=b\end{array}$

Step-3. Write the solution.

$\begin{array}{l}-23=b\\ \Rightarrow b=-23\end{array}$

Thus, the solution of the equation is $b=-23$.