Transcript x = -3

Math 015
Section 6.3
Equations
any algebra expressions on each side
variable terms on one side and
constants on the other side
by the coefficient of the variable
Obj: To solve an equation of the form
Problem:
Solution:
Solve
5x – 4 = 2x + 5
5x – 4 = 2x + 5
5x = 2x + 5 + 4
5x = 2x + 9
5x – 2x = 9
3x = 9
x= 9
3
x = -3
ax + b = cx + d
Obj: To solve an equation of the form
Problem:
Solution:
Solve
2y – 7 = -1 – 2y
2y – 7 = -2y – 1
2y = -2y + 6
4y = 6
x =
6
4
x =
3
2
ax + b = cx + d
Be sure to simplify each side before continuing the solving
process.
Problem:
Solve 5x – 2(x + 1) = 23
Solution:
5x – 2(x + 1) = 23
5x – 2x – 2 = 23
3x – 2 = 23
Simplify by combining like
terms on the left side
collect terms
3x = 25
divide
x = 25/3
Be sure to simplify each side before continuing the solving
process.
Problem:
Solution:
Solve 7 – (5 – 8x) = 4x + 3
7 – (5 – 8x) = 4x + 3
7 – 5 + 8x = 4x + 3
8x + 2 = 4x + 3
8x = 4x + 1
4x = 1
x = 1/4
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
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?
60
90
10 – x
x
90x = 60(10 – x )
90x = 600 – 60x
150x = 600
x = 4
The fulcrum must be 4 ft from
the 90 lb child.
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
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
x = 260
The company must build and
sell 260 barbecue units to
break even