Page 48 - Algebra 1

SOLUTION Simplify each expression. Then compare.
12+[5(7-5)3 -14] =12+[5(2)3 -14] = 12 + [5 · 8 - 14] = 12 + [40 - 14]
= 12 + 26 = 38
[(9-5)2 +7]-33 =[(4)2 +7]-33 = [16 + 7] - 33
= 23 - 33
= 23 - 27 = -4
Since38>-4,12+[5(7-5)3 -14] > [(9-5)2 +7]-33. Application: Half Price Sale
Beatrice wants to buy 3 DVDs marked $7 each and 4 CDs marked $12 each. Everything in the store is on sale for half off the marked price. Beatrice has $31.50 to spend and a coupon good for $1 off each CD. Use the expression below to determine if Beatrice has enough money to buy all the items she wants.
Example
5
Graphing Calculator
Enter the expression 10+8÷22 into
your calculator. If the calculator follows the order of operations, the answer will be 12.
__ $31.50-⎡⎢3·$7 + 4·$12 -(4·$1) ⎤
⎣22⎦
SOLUTION Begin inside the innermost symbols of inclusion to
simplify the expression. __
$31.50-⎢⎡3·$7 + 4·$12 -(4·$1) ⎤ ⎣22⎦
__
= $31.50 - ⎡⎢ 3 · $7 + 4 · $12 - $4⎤
Multiply inside the parentheses.
Simplify the numerators.
Simplify the fractions. Simplify inside the brackets. Subtract.
⎣22⎦ __
= $31.50 - ⎢⎡ $21 + $48 - $4⎤ ⎣22⎦
= $31.50 - [$10.50 + $24 - $4] = $31.50 - $30.50
= $1.00
Beatrice has enough money.
Simplify each expression.
(Ex 1)
a. 12+ 5-11
b. 5(8 + 4) ÷ (15 - 5 - 4)
c. 5 + [6 · (23 + 4)]
d. Justify Simplify the expression. Justify each_step. (Ex 3)
4(1+2)2 ÷6+ 8·3 2
Lesson Practice
Lesson 7 33