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When an integer is subtracted from times the next consecutive odd integer, the difference is . Find the value of the greater integer.Answer:
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Q. When an integer is subtracted from times the next consecutive odd integer, the difference is . Find the value of the greater integer.Answer:
- Define First Integer: Let's denote the first integer as . Since we are looking for the next consecutive odd integer, we need to consider two cases: if is odd, then the next consecutive odd integer is ; if is even, then the next consecutive odd integer is . However, since we are looking for an integer and the next consecutive odd integer, we can generalize this to because adding to any integer will always result in the next odd integer (if the integer is odd, it skips the even number; if the integer is even, it lands on the next odd).
- Set Up Equation: Now, let's set up the equation based on the problem statement: times the next consecutive odd integer minus the first integer equals .This gives us the equation: .
- Simplify and Solve: Next, we will simplify and solve the equation for .
- Isolate : Subtract from both sides of the equation to isolate the term with .
- Find : Now, divide both sides by to solve for .
- Find Greater Integer: We found that is , but we need to find the value of the greater integer, which is the next consecutive odd integer. Since is , the next consecutive odd integer is .
- Find Greater Integer: We found that is , but we need to find the value of the greater integer, which is the next consecutive odd integer. Since is , the next consecutive odd integer is .Therefore, the value of the greater integer is .
