Page 59 - Algebra 1

Two algebraic expressions are equivalent if they can be simplified to the same value. For example, 2 · 2 - 1 is equivalent to 15 ÷ 5. Both expressions have a simplified value of 3.
Comparing Algebraic Expressions
Compare the expressions when a = 4 and b = 3. Use <, >, or =. 3a2 + 2b - 4b3 2a2b2
SOLUTION Simplify the expression on the left and then compare. 3a2 +2b-4b3 2a2b2
3(4)2 + 2(3) - 4(3)3 2(4)2(3)2 =3(16)+2(3)-4(27) =2(16)(9) = 48 + 6 - 108 = 288
= 54 - 108
= -54
Since -54 < 288, 3a2 + 2b - 4b3 < 2a2b2 when a = 4 and b = 3. Many real-world situations can be described using math. Algebraic
expressions can be used to represent relationships between quantities.
Application: Phone Charges
A cell phone company charges a $20 monthly fee and then 45 cents per minute. The company uses the expression 20 + 0.45m to find the total amount to charge for each month. How much would the company charge for 200 minutes?
SOLUTION Substitute 200 for m in the expression and simplify.
20 + 0.45m
= 20 + 0.45(200) = 20 + 90
= 110
The cell phone company would charge $110.
Evaluate each expression for the given values.
Example
3
Example
4
Math Reasoning
Analyze In the expression 20 + 0.45m, what does the variable m represent?
Lesson Practice
a.
(Ex 1)
b.
(Ex 2)
c.
(Ex 3)
d.
(Ex 4)
3x-4b+2bx;x=10,b=2
2ab-4a2 +10;a=-1,b=8
Compare the expressions when x = 2 and y = 5. Use <, >, or =. (6x2 + y3) -3x6 8x4 - y3
44 Saxon Algebra 1
Climate The lowest recorded temperature is -89.4°C in Antarctica. The expression _9 C + 32 can be used to convert Celsius measurements
5
to Fahrenheit. What is the lowest recorded temperature in degrees Fahrenheit?