Download Section 2.4 Now You Can Solve Problems instead of just creating

Section 2.4
Now You Can
Solve Problems
instead of just
creating them!
Intro to Equations
 Equation
 Can be Numerical or Variable
 Has an equals sign or >, <.
 9+3=12
 3x-2=10
True or False
A true equation
x+8=13
If x = 5 then
5+8= 13 Note: this is true
True or False
 False Equation
 If 9+2y = 49
 So if we substitute 6 in for y
 Then 9+2*6 = 49
 This is a lie!
Solutions
 A solution to an equation is a number
that make the equation true.
 For example:
 Is 2 a solution of 2x-5=x2-3
 Lets find out by subbing in -2
 2*(2)-5 = (2)2-3

4-5 = 4-3

-1 = 1
More examples
 Is -4 a sol’n of 5x-2=6x+2
 5x-2=6x+2
 5(-4)-2 = 6(-4)+2

-20 -2 = -24 + 2

-22= -22
 YES!
Even more examples
 Is -4 a sol’n of 4+5x = x2-2x
 4+5x = x2-2x
 4+5(-4)=(-4)2-2(-4)
 4+(-20)=16-(-8)
 -16=24
 NO!
Give it a try
 Is (4) a solution to 5-4x=8x+2?
 Is 5 a solution of 10x-x2=3x-10
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

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
Is -6 a solution of 4x+3=2x-9
Yes
Is (-3) a solution of 4-6x=9x+1
No
Is -5 a solution of x2=25
Yes’m
Opposites
 Remember: solving algebraic
equations is all about opposites.
 i.e. do the opposite of the whatever
the mathematical operation is.
Solving Stuff
 What you want at the end of all your
work
 The variable to = a constant
 Like y=5
 What's the opposite of:






Addition
Subtraction
Multiplication
Division
Exponents
Square Roots
Square Roots
 Break it down
 Examples:
 Square roots of
49, 18, 27
 You try:
 Square roots of
44, 96, 45
Back to where we were
 First form
 X+a=b
X+3=5
Try to get simplify first (PEMDAS)
Try to isolate the variable
Do the opposite
X+3 =5
-3 -3
 X
=2





Example
 Y+3=2
 -3 -3

Y = -1
 Check your answer
 Sub in what you found for Y into the
original equation
Things are what they appear?
 3=T+5
 It’s the same thing– get everything
away from the variable.

3=T+ 5

-5
-5
 -2 =T
 Check your answer
Try These
5=x+5
 x=0
 X-(4) = 6
 X= 10
The second type
 Form ax=b
 2x=6
 What’s the operation between the 2 and the
x?
 What's the opposite?
 Do it!
 2x=6
 2 2
 x=3
You try it
 -2x = 6
 -3
 8x = 16
 2
 64 = 16x
 4
 2z = 0
 0
Applications and Formulas
 Turning words into equations
 The many words for “=“
 Equals, is equal to, is, represents,
was, is the same as
Processsssss
 1. Give the unknown a letter
 2. Break the problem down at the
“=“
 3. Translate as you read
 4. The “and”
Examples
 Negative fifty-six equals negative eight
times a number. Find the number.
 The high temperature today is 7 degrees
lower than the high temperature yesterday.
The high temperature today is -13. What
was the high temperature yesterday?
 A jeweler wants to make a profit of 250 on
the sale of a bracelet that cost 700. Use
 P = S – C where p is the profit, s is the
selling price, and c is the cost to find s.
You try it now
 The temperature now is 8 degrees lower than
yesterday. The temperature is -16 now. What was
the temperature yesterday?
 In the US, the average income of people 25 to 34 is
$14886 less than people 45 to 54. The average
income of people 24 to 34 is 41,414. Find the income
of the 45 to 54 year olds.
 The velocity (same as speed) of a falling object is
given by the formula v=gt2 where v is velocity, g is
gravity at 9.8 and t is time. What’s the velocity of a
rock falling for 3 seconds?
2.4 a Homework
 1 thru 47 eoo
 2, 10, 16, 26, 28, 32, 38, 42, 46, 50