Question

How do you find two consecutive even integers such that twice the smaller is 26 less than 3 times the larger?

Answer 1

Hint: Even integers are the integers that are completely divisible by 2. Consecutive even integers are integers following a sequence such that every subsequent number is 2 more than the preceding number. Form the equation from the statement given in the question and solve them to obtain the required result.

Complete step-by-step answer:
According to the question given, we need two consecutive even integers. Given that, the double of the smaller integer is less than the 3 times of the larger integer.
Remember even consecutive integers are the integers that follow a sequence that is every subsequent integer if always two more that its preceding integer.
Let assume the smaller even integer be $ x $ .Thus the even consecutive integer of $ x $ will be equal to $ x + 2 $
As per the question given, we are given that the double of the smaller integer is less than the 3 times of the larger integer. Form a mathematical equation showing this relation between both the even integers, we get the equation as
 $ \Rightarrow 2x = 3\left( {x + 2} \right) - 26 $
Resolving the brackets, we can rewrite the above equation as
 $ \Rightarrow 2x = 3x + 6 - 26 $
Combining all the like terms, we obtain
 $
   \Rightarrow 2x - 3x = 6 - 26 \\
   \Rightarrow - x = - 20 \\
   \Rightarrow x = 20 \;
  $
We got the smaller even integer as $ x = 20 $ . Now the consecutive even integer for $ x = 20 $ will be $ x + 2 = 20 + 2 = 22 $
Therefore, $ 20\,and\,22 $ are the required consecutive even integers .
So, the correct answer is “ $ 20\,and\,22 $ ”.

Note: 1.Mathematical equation: A Mathematical equation can be defined as the mathematical statement which contains an equal symbol $ = $ in between two algebraic expressions that share the same value .
A algebraic expression can contain any number of variables generally we take 2-3 variables
Let assume a expression
 $ 5x + 9 = 24 $
It is a mathematical equation having LHS (Left-Hand-Side) equal to RHS (Right-Hand-Side)
Where $ x $ is the variable
5 is the coefficient of variable $ x $
And $ 24,9 $ are the constants
2. Read the statement carefully in order to convert them into mathematical expressions.
3.In order to solve such types of questions we should know the concept of consecutive numbers .
4. Most common mistake many people make in such problems is in the calculation part. So, Avoid calculation mistakes while solving such problems .