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The sum of three consecutive even integers is 0 . Find the value of the least of the three. Answer:

The sum of three consecutive even integers is 00 . Find the value of the least of the three.\newlineAnswer:

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Full solution

Q. The sum of three consecutive even integers is 00 . Find the value of the least of the three.\newlineAnswer:
  1. Identify First Even Integer: Let xx be the first even integer. Since we are dealing with consecutive even integers, the next two integers would be x+2x+2 and x+4x+4. Consecutive even integers: xx, x+2x+2, x+4x+4
  2. Set Up Equation: Set up an equation that represents the sum of the three consecutive even integers equal to 00.\newlineEquation: x+(x+2)+(x+4)=0x + (x+2) + (x+4) = 0
  3. Simplify Equation: Simplify the left side of the equation x+(x+2)+(x+4)=0x + (x+2) + (x+4) = 0.x+(x+2)+(x+4)=0x + (x+2) + (x+4) = 0(x+x+x)+(2+4)=0(x + x + x) + (2+4) = 03x+6=03x + 6 = 0
  4. Isolate Variable Term: Isolate the variable term in 3x+6=03x + 6 = 0.
    3x+6=03x + 6 = 0
    3x+6−6=0−63x + 6 - 6 = 0 - 6
    3x=−63x = -6
  5. Solve for x: Solve for x.\newline3x=−63x = -6\newline3x3=−63\frac{3x}{3} = \frac{-6}{3}\newlinex=−2x = -2
  6. Final Result: We have found that x=−2x = -2. This is the value of the least of the three consecutive even integers.\newlineThe three consecutive even integers are:\newlinex,x+2,x+4x, x+2, x+4\newline−2,−2+2,−2+4-2, -2+2, -2+4\newline−2,0,2-2, 0, 2

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