To find the largest among three consecutive integers whose sum is 30, follow these steps:
1. Consider Three Consecutive Integers:
Let the three consecutive integers be [tex]\( x \)[/tex], [tex]\( x + 1 \)[/tex], and [tex]\( x + 2 \)[/tex].
2. Set Up the Equation:
The sum of these three integers is given as 30. Therefore, we can write the equation:
[tex]\[
x + (x + 1) + (x + 2) = 30
\][/tex]
3. Combine Like Terms:
Simplify the equation by combining like terms:
[tex]\[
x + x + 1 + x + 2 = 30
\][/tex]
[tex]\[
3x + 3 = 30
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
First, subtract 3 from both sides of the equation to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
3x + 3 - 3 = 30 - 3
\][/tex]
[tex]\[
3x = 27
\][/tex]
Next, divide both sides by 3 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 9
\][/tex]
5. Identify the Three Consecutive Integers:
If [tex]\( x \)[/tex] is 9, then the three consecutive integers are:
[tex]\[
x = 9
\][/tex]
[tex]\[
x + 1 = 10
\][/tex]
[tex]\[
x + 2 = 11
\][/tex]
6. Determine the Largest Integer:
Among the integers 9, 10, and 11, the largest is 11.
Therefore, the largest among the three consecutive integers whose sum is 30 is [tex]\( 11 \)[/tex].
