Chapter 1.1, Problem 32E

To determine

To solve the equation $b-\frac{3}{16}=\frac{5}{16}$ by justifying each step.

Answer to Problem 32E

  $b=\frac{1}{2}$

Explanation of Solution

Given information :

Consider the equation $b-\frac{3}{16}=\frac{5}{16}$ .

Calculations:

Multiply the equation by 16.

  $\Rightarrow 16\cdot \left(b-\frac{3}{16}\right)=16\cdot \frac{5}{16}$

Apply distributive property.

  $\Rightarrow 16b-3=5$

Add 3 on both sides of the equation.

  $\begin{array}{l}\Rightarrow 16b-3+3=5+3\\ \Rightarrow 16b=8\end{array}$

Divide the equation by 16 and simplify the expression.

  $\begin{array}{l}\Rightarrow \frac{16b}{16}=\frac{8}{16}\\ \Rightarrow b=\frac{1}{2}\end{array}$

To check the solution, back-substitute $\frac{1}{2}$ for $b$ in the equation $b-\frac{3}{16}=\frac{5}{16}$ .

  $\begin{array}{l}\left(\frac{1}{2}\right)-\frac{3}{16}\stackrel{?}{=}\frac{5}{16}\\ \frac{8}{16}-\frac{3}{16}\stackrel{?}{=}\frac{5}{16}\\ \frac{8-3}{16}\stackrel{?}{=}\frac{5}{16}\\ \frac{5}{16}=\frac{5}{16}\text{True}\end{array}$