Beginning Algebra, 11th Edition

SECTION 2.4 An Introduction to Applications of Linear Equations^113

Step 5 State the answer.The lesser page number is 112, and the greater page

number is (Your book is opened to these two pages.)

Step 6 Check.The sum of 112 and 113 is 225. The answer is correct.

NOW TRY

Consecutiveevenintegers,such as 8 and 10, differ by 2. Similarly, consecutive

oddintegers,such as 9 and 11, also differ by 2. See FIGURE 4.

In general, if x represents an even or odd integer, represents the next

greater consecutive even or odd integer, respectively.

In this book, we list consecutive integers in increasing order.

x 2

112 + 1 = 113.

NOW TRY
EXERCISE 6
Two pages that face each
other have 593 as the sum of
their page numbers. What are
the page numbers?

0 15

xx 2

234

2 units

Consecutive even integers

Consecutive odd integers

FIGURE 4 If the lesser integer, then, for any

two consecutive integers, use x,

two consecutive evenintegers, use x,

two consecutive oddintegers, use x, x2.

x2;

x1;

x=

PROBLEM-SOLVING HINT

Finding Consecutive Odd Integers

If the lesser of two consecutive odd integers is doubled, the result is 7 more than the

greater of the two integers. Find the two integers.

Let xbe the lesser integer. Since the two numbers are consecutive oddintegers,

then is the greater. Now we write an equation.

If the lesser more the is doubled, the result is 7 than greater.

2 x 7

Combine like terms. Subtract x.

The lesser integer is 9 and the greater is As a check, when 9 is doubled,

we get 18, which is 7 more than the greater odd integer, 11. The answers are correct.

NOW TRY

9 + 2 = 11.

x= 9

2 x= 9 +x

= + 1 x+ 22

x+ 2

NOW TRY EXAMPLE 7

EXERCISE 7
Find two consecutive odd
integers such that the sum of
twice the lesser and three
times the greater is 191.

1 2

Angles and are complementary. They form a right angle.

1 2 Angles and are supplementary. They form a straight angle.

3 4

3 4 Straight angle

180 °

FIGURE 5

NOW TRY ANSWERS

296, 297 7.37, 39

OBJECTIVE 5 Solve problems involving supplementary and complemen-

tary angles.An angle can be measured by a unit called the degree , which is

of a complete rotation. Two angles whose sum is 90° are said to be complementary,

or complementsof each other. An angle that measures 90° is a right angle.Two an-

gles whose sum is 180° are said to be supplementary,or supplementsof each other.

One angle supplementsthe other to form a straight angleof 180°. See FIGURE 5.

1

1 ° (^2360)
denotes a
90° or right angle.
m