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There are $3$ consecutive integers with a sum of $18$ . Which integers are they? $\newline$ $\_$ , $\_$ , $\_$

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Consecutive integer problems

Full solution

Q. There are

3

consecutive integers with a sum of

18

. Which integers are they?

\newline

\_

,

\_

,

\_

Identify First Integer: 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 $18$ ? $\newline$ Add three consecutive integers and equate the sum to $18$ . $\newline$ Equation: $x + (x+1) + (x+2) = 18$
Simplify Equation: Simplify the left side of $x + (x+1) + (x+2) = 18$ . $\newline$ $x + (x+1) + (x+2) = 18$ $\newline$ $(x + x + x) + (1+2) = 18$ $\newline$ $3x + 3 = 18$
Isolate Variable Term: Isolate the variable term in $3x + 3 = 18$ . $\newline$ $3x + 3 = 18$ $\newline$ $3x + 3 - 3 = 18 - 3$ $\newline$ $3x = 15$
Solve for x: $3x = 15$ $\newline$ Solve for x. $\newline$ $3x = 15$ $\newline$ $(3x)/3 = 15/3$ $\newline$ $x = 5$
Final Consecutive Integers: We have: $\newline$ $x = 5$ $\newline$ What are the $3$ consecutive integers that add up to $18$ ? $\newline$ Three consecutive integers: $\newline$ $x, x+1, x+2$ $\newline$ $5, 5+1, 5+2$ $\newline$ $5, 6, 7$

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