Math 015 Section 6.3 Equations

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Math 015 Section 6.3 Equations
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Remember!
Simplify
any algebra expressions on each side
variable terms on one side and constants on the
other side
Collect
Divide
by the coefficient of the variable
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Obj To solve an equation of the form ax b
cx d
Problem Solve 5x 4 2x 5
Solution
5x 4 2x 5
5x 2x 5 4
5x 2x 9
5x 2x 9
3x 9
9 3
x
x -3
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Obj To solve an equation of the form ax b
cx d
Problem Solve 2y 7 -1 2y
Solution
2y 7 -2y 1
2y -2y 6
4y 6
6
x
4
32
x
5
Be sure to simplify each side before continuing
the solving process.
Problem Solve 5x 2(x 1) 23
Solution
5x 2(x 1) 23
Simplify by combining like terms on the left side
5x 2x 2 23
collect terms
3x 2 23
3x 25
divide
x 25/3
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Be sure to simplify each side before continuing
the solving process.
Problem Solve 7 (5 8x) 4x 3
Solution
7 (5 8x) 4x 3
7 5 8x 4x 3
8x 2 4x 3
8x 4x 1
4x 1
x 1/4
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Lever System Equation
F1x F2(d x)
F1 weight (force) of one object F2 weight
(force) of the second object
d length of the lever
x distance from F1 to the fulcrum
d x distance from F to the fulcrum
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Lever System Equation
F1x F2(d x)
Two children are sitting on a seesaw that is 10
ft long. One child weighs 60 lb and the other
child weighs 90 lb. How far from the 90 lb child
should the fulcrum be placed for them to balance?
90
60
x
10 x
90x 60(10 x )
90x 600 60x
150x 600
The fulcrum must be 4 ft from the 90 lb child.
x 4
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Break-even point
Px Cx F
x the number of things produced
P the selling price for each unit
C the cost to produce each unit
F the fixed cost for the business
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Break-even point
Px Cx F
An economist has determined that the selling
price per unit for a gas barbecue is 325. The
cost to make one barbecue is 175, and the fixed
cost for the factory is 39,000. Find the
break-even point.
325x 175x 39,000
150x 39,000
The company must build and sell 260 barbecue
units to break even
x 260