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There are $3$ consecutive integers with a sum of $9$ . What are the integers? $\newline$ $\_\_\_\_\_$ , $\_\_\_\_\_$ , $\_\_\_\_\_$

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Consecutive integer problems

Full solution

Q. There are

3

consecutive integers with a sum of

9

. What are the integers?

\newline

\_\_\_\_\_

,

\_\_\_\_\_

,

\_\_\_\_\_

Define Integers: Let $x$ be the first integer. $\newline$ Which represents the three consecutive integers? $\newline$ Consecutive integers increase by $1$ each time. $\newline$ Consecutive integers: $x$ , $x+1$ , $x+2$
Sum of Consecutive Integers: Which equation represents the sum of $3$ consecutive integers is $9$ ? $\newline$ Add three consecutive integers and equate the sum to $9$ . $\newline$ Equation: $x + (x+1) + (x+2) = 9$
Simplify Equation: Simplify the left side of $x + (x+1) + (x+2) = 9$ . $\newline$ $x + (x+1) + (x+2) = 9$ $\newline$ $(x + x + x) + (1+2) = 9$ $\newline$ $3x + 3 = 9$
Isolate Variable Term: Isolate the variable term in $3x + 3 = 9$ .
$3x + 3 = 9$
$3x + 3 - 3 = 9 - 3$
$3x = 6$
Solve for x: $3x = 6$ $\newline$ Solve for x. $\newline$ $3x = 6$ $\newline$ $(3x)/3 = 6/3$ $\newline$ $x = 2$
Identify Consecutive Integers: We have: $\newline$ $x = 2$ $\newline$ What are the $3$ consecutive integers that add up to $9$ ? $\newline$ Three consecutive integers: $\newline$ $x, x+1, x+2$ $\newline$ $2, 2+1, 2+2$ $\newline$ $2, 3, 4$

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