Chapter 4.2, Problem 10P

To determine

To find: the integers where the greater of two consecutive even integers is 10 less than twice the

smaller.

Answer to Problem 10P

The required answer is: consecutive even integers are 12 and 14

Explanation of Solution

Calculation:

Let the smaller even integer be x

Let the greater even integer be x+2

  $x+2=2x-10$

(Greater integer is 10 less than twice the smaller integer)

  $x+2-2=2x-10-2$

(Subtract 2 from both sides)

  $\begin{array}{l}x=2x-12\\ x-x=2x-12-x\end{array}$

(Subtract x from both sides)

  $\begin{array}{l}0=x-12\\ 0+12=x-12+12\end{array}$

(Add 12 to both sides)

  $12=x$

(Simplify)

Smaller integer:

  $x=12$

Greater integer:

  $\begin{array}{l}x+2=12+2\\ x+2=14\end{array}$

Therefore the consecutive even integers are 12 and 14.