Which of the following did you include in your description? Check all of the boxes that apply.Let x = the smallest even integer, x + 2 = the next even integer, and x + 4 = the largest even integer.Write the equation x + x + 2 + x + 4 = –78.Simplify the equation as 3x + 6 = –78.Solve the equation by subtracting 6 and dividing by 3 on both sides of the equation.Check that the sum of the integers –28, –26, and –24 is –78.
Answer
A
Let x = the smallest even integer, x + 2 = the next even integer, and x + 4 = the largest even integer.
B
Write the equation x + x + 2 + x + 4 = –78.
C
Simplify the equation as 3x + 6 = –78.
D
Solve the equation by subtracting 6 and dividing by 3 on both sides of the equation.
E
Check that the sum of the integers –28, –26, and –24 is –78.
Explanation
All five statements describe valid steps for solving the problem. The three consecutive even integers can be written as x, x + 2, and x + 4, so their sum gives x + (x + 2) + (x + 4) = −78, or 3x + 6 = −78. Subtracting 6 and dividing by 3 gives x = −28, so the integers are −28, −26, and −24; their sum is −78.
AI-written and checked against the verified answer.