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Three consecutive integers sum to $24$ . Which integers are they? $\newline$ $\_\_\_\_\_$ , $\_\_\_\_\_$ , $\_\_\_\_\_$

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Consecutive integer problems

Full solution

Q. Three consecutive integers sum to

24

. Which integers are they?

\newline

\_\_\_\_\_

,

\_\_\_\_\_

,

\_\_\_\_\_

Define Integers: Let $x$ be the first integer. The three consecutive integers can be represented as $x$ , $x+1$ , and $x+2$ .
Set Up Equation: Set up the equation to represent the sum of the three consecutive integers equal to $24$ : $x + (x+1) + (x+2) = 24$ .
Simplify Equation: Simplify the equation: $x + x + 1 + x + 2 = 24$ . Combine like terms: $3x + 3 = 24$ .
Isolate Variable Term: Isolate the variable term by subtracting $3$ from both sides of the equation: $3x + 3 - 3 = 24 - 3$ . This simplifies to $3x = 21$ .
Divide to Solve: Divide both sides of the equation by $3$ to solve for $x$ : $\frac{3x}{3} = \frac{21}{3}$ . This gives us $x = 7$ .
Find Consecutive Integers: Now that we have the value of $x$ , we can find the three consecutive integers: $x$ , $x+1$ , and $x+2$ . Substitute $x$ with $7$ : $7$ , $7+1$ , $7+2$ . This gives us the integers: $7$ , $x$ $0$ , $x$ $1$ .

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