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The sum of an integer and times the next consecutive even integer is . Find the value of the lesser integer.Answer:
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Q. The sum of an integer and times the next consecutive even integer is . Find the value of the lesser integer.Answer:
- Identify Integers: Let's denote the lesser integer as . Since we are looking for consecutive even integers, the next consecutive even integer would be . The problem states that the sum of the lesser integer and times the next consecutive even integer is . We can write this as an equation:
- Write Equation: Now, let's distribute the into the parentheses:
- Distribute and Simplify: Combine like terms to simplify the equation:
- Isolate Variable: Subtract from both sides to isolate the term with the variable:
- Solve for x: Divide both sides by to solve for x:
- Check Solution: We have found the value of the lesser integer, which is . To ensure that we have not made any mistakes, let's check our solution by plugging it back into the original equation:The solution checks out.
