Fundamentals of Mathematics, 2008a

664 CHAPTER 11. ALGEBRAIC EXPRESSIONS AND EQUATIONS
Step 4: Check this result.
Three times −2 is −6. Increasing −6 by 4 results in −6 + 4 = −2. Now, ve times −2 is −10.
Increasing −10 by 8 results in −10 + 8 = −2. The results agree, and the solution checks.
Step 5: The number is −2
Example 11.46
Consecutive integers have the property that if
n = the smallest integer, then
n + 1 = the next integer, and
n + 2 = the next integer, and so on.
Consecutive odd or even integers have the property that if
n = the smallest integer, then
n + 2 = the next odd or even integer (since odd or even numbers dier by 2), and
n + 4 = the next odd or even integer, and so on.
The sum of three consecutive odd integers is equal to one less than twice the rst odd integer. Find
the three integers.
Step 1.
Let n = the rst odd integer. Then,
n + 2 = the second odd integer, and
n + 4 = the third odd integer.
Step 2. Translate the words to mathematical symbols and construct an equation.
Step 3.
The sum of:
add some numbers
three consecutive odd integers: n, n + 2, n + 4
is equal to: =
one less than:
twice the rst odd integer:
n + n + 2 + n + 4 = 2n − 1
3n + 6 = 2n − 1
3n + 6 − 2n = 2n − 1 − 2n
n + 6 = −1
n + 6 − 6 = −1 − 6
subtract 1 from
2n
Subtract 2n from both sides.
Subtract 6 from both sides.
n = −7 The rst integer is -7.
n + 2 = −7 + 2 = −5 The second integer is -5.
n + 4 = −7 + 4 = −3 The third integer is -3.
Step 4. Check this result.
The sum of the three integers is
−7 + (−5) + (−3) = −12 + (−3)
Read phrases.
}n + (n + 2) + (n + 4) = 2n − 1
= −15
One less than twice the rst integer is 2 (−7) − 1 = −14 − 1 = −15. Since these two results
are equal, the solution checks.
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