To solve the problem, let’s denote the first integer as [tex]\( x \)[/tex]. The next three consecutive integers would then be logically [tex]\( x + 1 \)[/tex], [tex]\( x + 2 \)[/tex], and [tex]\( x + 3 \)[/tex].
We need to fill in the table by following these steps:
1. Identify the four consecutive integers starting from [tex]\( x \)[/tex]:
- First integer: [tex]\( x \)[/tex]
- Second integer: [tex]\( x + 1 \)[/tex]
- Third integer: [tex]\( x + 2 \)[/tex]
- Fourth integer: [tex]\( x + 3 \)[/tex]
2. Calculate the indicated sum of the second, third, and fourth integers:
- Second integer: [tex]\( x + 1 \)[/tex]
- Third integer: [tex]\( x + 2 \)[/tex]
- Fourth integer: [tex]\( x + 3 \)[/tex]
Adding these together:
[tex]\[
(x + 1) + (x + 2) + (x + 3)
\][/tex]
3. Simplify the sum:
- Combine like terms:
[tex]\[
x + 1 + x + 2 + x + 3 = 3x + 6
\][/tex]
So, the simplified expression for the sum of the second, third, and fourth consecutive integers is [tex]\( 3x + 6 \)[/tex].
Here is the filled-in table:
\begin{tabular}{|c|c|c|c|}
\hline
First Integer & \multicolumn{3}{|c|}{Next Integers} \\
\hline
Integer: & [tex]\( x + 1 \)[/tex] & [tex]\( x + 2 \)[/tex] & [tex]\( x + 3 \)[/tex] \\
\hline
\end{tabular}
Now, the completed statement:
Sum of the second, third, and fourth consecutive integers, simplified:
[tex]\( 3x + 6 \)[/tex]
