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When an integer is subtracted from 5 times the next consecutive even integer, the difference is -22. Find the value of the lesser integer. Answer:

When an integer is subtracted from 55 times the next consecutive even integer, the difference is −22-22. Find the value of the lesser integer.\newlineAnswer:

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Full solution

Q. When an integer is subtracted from 55 times the next consecutive even integer, the difference is −22-22. Find the value of the lesser integer.\newlineAnswer:
  1. Denote integers: Let's denote the lesser integer as xx. Since we are dealing with consecutive even integers, the next consecutive even integer would be x+2x + 2. The problem states that 55 times the next consecutive even integer minus the lesser integer equals −22-22. We can write this as an equation:\newline5(x+2)−x=−225(x + 2) - x = -22
  2. Write equation: Now, let's distribute the 55 into the parentheses: 5x+10−x=−225x + 10 - x = -22
  3. Distribute 55: Next, we combine like terms on the left side of the equation: 4x+10=−224x + 10 = -22
  4. Combine like terms: To isolate the variable xx, we need to subtract 1010 from both sides of the equation:\newline4x+10−10=−22−104x + 10 - 10 = -22 - 10\newline4x=−324x = -32
  5. Isolate variable xx: Finally, we divide both sides of the equation by 44 to solve for xx:4x4=−324\frac{4x}{4} = \frac{-32}{4}x=−8x = -8

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