Transcript solve an equation

Section 1.2
Solving Equations Using
A Graphing Utility
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OBJECTIVE 1
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• Equations in one variable:
x5  9
x2  5x  2 x  2
x2  4
0
x 1
• Values of the variable, if any, that result in a true statement are
called solutions, or roots
• To solve an equation means to find the solutions of the
equation
• Identity is an equation that is true for any value for the
variable
2x + 3 = 3x + 1 – x + 2
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Find the solution(s) to the equation
x3  5 x  1  0
Approximate to two decimal places.
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Find the solution(s) to the equation
x 2  3  x3  1
Approximate to two decimal places.
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Solve the equations both algebraically and graphically:
a ) 4  2 x  1  3  3 x  2 
( Using Xmin: -12, Xmax: 0, Xscl: 2, Ymin:-100, Ymax: 0, Yscl: 10)
b) ( x  7)( x  1)  ( x  1) 2
( Using Xmin: -5, Xmax: 3, Xscl: 1, Ymin: -5, Ymax: 15, Yscl: 1)
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Solving an Equation Algebraically
Solve the linear equations
(a) 2(2x - 3) = 3(x – 1)
(b) (x +3)(x – 2) = (x + 2)2
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Solving an Equation Algebraically
Solve the rational equations
(a)
(b)
4
3
7


x  2 x  5 ( x  5)( x  2)
x
2
3
x2
x2
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Solve the rational equations
4
3
7


x  2 x  5 ( x  5)( x  2)
4
3
7
 ( x  5)( x  2) 
 ( x  5)( x  2) 
x2
x5
( x  5)( x  2)
4( x  5)  3( x  2)  7
( x  5)( x  2) 
4 x  20  3 x  6  7
7 x  13  20
7 x  7
x  1
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Solve the rational equations
x
2
3
x2
x2
x
2
( x  2) 
 ( x  2)  3  ( x  2) 
x2
x2
x  3( x  2)  2
x  3x  6  2
4x  8
NOT a solution
x2
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• Solving Problems That Can Be Modeled By Linear
Equations
Problem Solving Procedure
• Understand the problem
– Read it twice
– What are you asked to find
– What information is pertinent
• Translate problem into algebraic expression or equation or
formula to use
• Carry out mathematical calculation
• Check answer – is it reasonable?
• Make sure you answered the question
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•
Judy and Tom agree to share the cost of an $18 pizza based
based on how much each ate. If Tom ate 2/3 the amount
that Judy ate, how much should each pay? (Page 112 #98)
J + 2/3J = $18
5/3J = $18
J = 18(3/5) = $10.80
• Jim is paid time-and-a-half for hours worked in excess
of 40 hours and double-time for hours worked on Sunday. If Jim
had gross weekly wages of $806.55 for working 50 hours, 4 of
which were on Sunday, what is his regular hourly rate? (Page 112
#100)
40r + 6(1.5r) + 4(2r) = 806.55
57r = 806.55
r = 14.15
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