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When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 5 . Find the value of the lesser integer.
Answer:

When an integer is subtracted from 44 times the next consecutive odd integer, the difference is 55 . Find the value of the lesser integer.\newlineAnswer:

Full solution

Q. When an integer is subtracted from 44 times the next consecutive odd integer, the difference is 55 . Find the value of the lesser integer.\newlineAnswer:
  1. Denote lesser integer as 'n': Let's denote the lesser integer as '\newline'. The next consecutive odd integer can be represented as '\newline + 22' because odd integers are two units apart. According to the problem, 44 times the next consecutive odd integer minus the lesser integer equals 55. We can write this as an equation:\newline4(n+2)n=54(n + 2) - n = 5
  2. Represent next odd integer: Now, let's distribute the 44 into the parentheses: 4n+8n=54n + 8 - n = 5
  3. Write equation with integers: Next, we combine like terms on the left side of the equation: 4nn+8=54n - n + 8 = 5 3n+8=53n + 8 = 5
  4. Distribute 44 into parentheses: We then isolate the variable nn by subtracting 88 from both sides of the equation:\newline3n+88=583n + 8 - 8 = 5 - 8\newline3n=33n = -3
  5. Combine like terms: Finally, we divide both sides of the equation by 33 to solve for 'nn':\newline3n3=33\frac{3n}{3} = \frac{-3}{3}\newlinen=1n = -1

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