Math Help for Section 3.2, Page 110

Equations
Containing Symbols of Grouping
Recall that symbols of grouping include parentheses, brackets, and
fraction bars.

Example
1: Check

$\eqalign{ {\textbf{a.}\quad\quad}4\left( {x – 3}
\right) =& 8&{\small\color{red}\quad\quad\text{Write
original equation.}}  \cr 4\left( {\color{red}5\color{black}
– 3} \right) \overset{?}{=}&
8&{\small\color{red}\quad\quad\text{Substitute 5
for }x.}  \cr 4\left( 2
\right) \overset{?}{=}&
8&{\small\color{red}\quad\quad\text{Subtract.}}  \cr 8
=& 8&{\small\color{red}\quad\quad\text{Solution
checks. }\checkmark} \cr}$

$\eqalign{ {\textbf{b.}\quad\quad} 3\left( {2x – 1} \right) + x
=& 11&{\small\color{red}\quad\quad\text{Write
original equation.}}  \cr 3\left[ {2\left(
\color{red}2\color{black} \right) – 1} \right]
+ \color{red}2\color{black}
\overset{?}{=}&
11&{\small\color{red}\quad\quad\text{Substitute 2
for }x.}  \cr 3\left( {4 – 1} \right) +
2 \overset{?}{=}&
11&{\small\color{red}\quad\quad\text{Multiply.}}  \cr
3\left( 3 \right) + 2 \overset{?}{=}&
11&{\small\color{red}\quad\quad\text{Subtract.}}  \cr
9
+ 2 \overset{?}{=}&
11&{\small\color{red}\quad\quad\text{Multiply.}}  \cr
11 =&
11&{\small\color{red}\quad\quad\text{Solution
checks. }\checkmark} \cr} $

Notice in the checks that you do not need to use the Distributive
Property to remove the parentheses. Simply evaluate the expression
within the parentheses and then multiply.