Page 181 - Algebra 1

No Solutions or Infinitely Many Solutions
Solve each equation. Justify each step.
Example
3
a. 10-6x=-2(3x-5) SOLUTION
10 - 6x = -2(3x - 5) 10 - 6x = -6x + 10
+_6_x =+_6_x 10 = 10
Distributive Property Addition Property of Equality Simplify. Always true.
Math Reasoning
Analyze When the simplified equation is an identity, what values of the variable will satisfy the original equation?
Since 10 = 10 is always true, the equation is an identity.
Math Reasoning
Analyze When all variables are eliminated in an equation, resulting in a false statement, what values of the variable satisfy the original equation?
166 Saxon Algebra 1
b. 7x-2=9x-5-2x SOLUTION
7x - 2 = 9x - 5 - 2x 7x - 2 = 7x - 5
-_7_x = -_7_x -2 = -5
Combine like terms. Addition Property of Equality Simplify. Never true.
Since -2 = -5 is never true, the equation has no solutions. Application: Telephone Rates
Telephone Company A charges $18.95 per month for local calls and $0.04 per minute for long-distance calls. Telephone Company B charges $21.95 per month for local calls and $0.02 per minute for long-distance calls. For what number of minutes of long-distance calls per month is the cost of the plans the same?
SOLUTION
Let m = the number of minutes of long distance calls. Company A’s monthly charge = $18.95 + $0.04m Company B’s monthly charge = $21.95 + $0.02m
Example
4
18.95 + 0.04m = 21.95 + 0.02m -_ 0 _ . 0 _ 2 _ m = -_ 0 _ . 0 _ 2 _ m
18.95 + 0.02m = 21.95
Write an equation.
Subtraction Property of Equality Simplify.
Subtraction Property of Equality Simplify.
Division Property of Equality
Simplify.
-_ _ 1 8 _ . 9 _ 5
= -_ _ 1 8 _ . 9 _ 5
0.02m = 3.00
0.02m = 3.00 __
0.02m 0.02 m = 150
The costs will be same for 150 minutes.