Transcript Literal Equations

LITERAL EQUATIONS
Isolate an indicated variable in an
equation.
Learning Goal for Focus 2
(HS.A-CED.A.1, 2 & 3, HS.A-REI.A.1, HS.A-REI.B.3):
The student will create equations from multiple representations and solve
linear equations and inequalities in one variable explaining the logic in each
step.
4
3
2
1
0
In addition to
level 3.0 and
above and
beyond what was
taught in
class, the
student may:
- Make
connection with
other concepts
in math
- Make
connection with
other content
areas.
The student will
create equations
from multiple
representations and
solve linear equations
and inequalities in one
variable explaining
the logic in each step.
- rearrange formulas
to highlight a quantity
of interest.
-Graph created
equations on a
coordinate graph.
The student will
be able to solve
linear equations
and inequalities in
one variable and
explain the logic
in each step.
- Use equations
and
inequalities in
one variable to
solve
problems.
With help
from the
teacher,
the student
has
partial
success
with solving
linear
equations
and
inequalities
in one
variable.
Even with
help, the
student
has no
success
with
solving
linear
equations
and
inequalities
in one
variable.
Formulas
• There are many formulas that you have used
so far in your math career. Here are a few:
• D = rt
• A = bh
• A = ½ h(b1 + b2)
• I = Prt
• V = LWH
• SA = 2LW + 2LH + 2WH
• Our goal is to be able to rearrange formulas to
isolate a desired variable.
• Use the properties of algebra to do this
“legitimately.”
Image from http://varner.typepad.com/mendenhall/
Isolate “u” in the following equations. Give a
property to justify each step.
•
•
•
•
1/
3u
–8=y
1/ u = y + 8
• Addition Property (add 8)
3
u = 3(y + 8)
• Multiplication Property (•3)
***That is the final answer. All
you have to do is isolate the
indicated variable. You will not
SOLVE it.***
• w = 9 + 14ux
• w – 9 = 14ux
• (w – 9) = u
14x
• Subtraction Property (- 9)
• Division Property (÷ 14x)
• This is the final answer. 
Image from http://varner.typepad.com/mendenhall/
Isolate “w” in the following equations. Give a
property to justify each step.
• y = 2x + w
v
• vy = 2x + w
• Multiplication Property (•v)
• vy – 2x = w
• Subtraction Property (-2x)
• w+x=y
3
• w=y–x
3
• w = 3(y – x)
• Subtraction Property (-x)
• Multiplication Property (•3)
Image from http://varner.typepad.com/mendenhall/
Isolate “m” in the following equation. Give a
property to justify each step.
•k = am + 3mx
•k = m(a + 3x)
•
k =m
a + 3x
• The “m” is in both terms. It is a
factor of both terms. You will
need to “factor it out of them.”
This is the distributive property
backwards.
• Distributive Property
• Division Property (÷ [a + 3x])
Image from http://varner.typepad.com/mendenhall/