Question

Ind two consecutive even integers such that twice the lesser of two integers is 4 less than two times the greater integer. a. Write and solve an equation to find the integers. Multiple choice question. A) 2n−4=2(n+2); true for all even integers B) 2n=2(n+2)−4; true for some even integers C) 2n=2(n+2)−4; true for all even integers D) 2n−4=2(n+2); true for some even integers Part B Feedback Incorrect 2 tries left. Please try again. Select the correct choices to complete the sentence. b. Does the equation have one solution, no solution, or is it an identity? Explain. It , 1 of 2. is an identity because it is , 2 of 2. false for every pair of consecutive even integers.

Answer 1

Explanation:

Let the consecutive even integers be 2n and 2n+2.

lesser integer = 2n

Greater integer = 2n+2

If twice the lesser of two integers is 4 less than two times the greater integer, this is expressed mathematically as;

2(less integer) = 2(greater integer) - 4

Substituting the given integers;

2(2n) = 2(2n+2)-4

2(2n) = 2[(2n+2)-2]

2n = 2n+2-2

2n = 2n

2 = 2

This two values cancels out and become 0 = 0. This equality shows that it is an identity pair and it is true for all even integers.