One way to write an expression is by calculating the number of x-terms and 1s in the whole diagram.
Example Solutions: 3x+12 or 3(x+4)
Practice makes perfect
Before we begin, note that there are more than two correct solutions to this exercise. Here, we will write only two possible expressions.
First Expression
The given diagram sho
ws three rows, each composed of an x and four 1s. One way we can create an expression is by grouping the x variables and the 1s separately.
\begin{aligned}
&\boxed{\phantom{11}{\color{#0000FF}{x}}\phantom{11}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\\
&\boxed{\phantom{11}{\color{#0000FF}{x}}\phantom{11}
}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\\
&\boxed{\phantom{11}{\color{#0000FF}{x}}\phantom{11}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}\boxed{\phantom{1}{\color{#FF0000}{1}}\phantom{1}}
\end{aligned}
In total there are three x-terms and twelve 1s, so we can form the following expression.
3x+ 12
Second Expression
Another way we can create an expression is by looking at each row as its own grouping.
&x1111
&x1111
&x1111
In this case, the expression that corresponds to each row is x+4. Since there are three rows, by multiplying it by 3 we can write the second possible expression for the whole diagram.
3(x+4)
