Literal EquationsAn Introduction
Copyright 2014 Scott Storla
Definition of a Literal Equation
A literal equation has at least two different letters that stand for variables.
Copyright 2014 Scott Storla
2 2Perimeter of a rectangle P L W
Money earned from an investment ertA P
20 3 0 8 3 4Percent using online banking . . . y x x
Notation
20.75 4.2 10.83 P p
0 is different from A A
In literal equations capital and small letters that are similar represent different things.
A letter with a subscript is different from the same letter without the subscript.
Copyright 2014 Scott Storla
1 2 has a different value than x x
The same letter with different subscripts represents two different values for the same variable.
A literal equation is “solved for” one of the variables.
Copyright 2014 Scott Storla
2 2 P L W
2
2
P wL
1
2W P L
Solved for P
Solved for L
Solved for W
2 2P L W
2 2L L
2 2
Solve 2 2 for .P L W W
2 2P L W
Copyright 2014 Scott Storla
Operation Inverse
22L 2L
2
2
2
P LW
Literal EquationsAn Introduction
Copyright 2014 Scott Storla
Literal EquationsPractice
Copyright 2014 Scott Storla
m my b mx
b b
Solve for .y mx b x
y mx b
Copyright 2014 Scott Storla
Oper Inv
m m
b b
y bx
m
2 1
1
L NLW
L
2 1Solve for .
NW N
L
2 1NW
L
Copyright 2014 Scott Storla
Oper Inv
2 2
1 1
L L
2 1N LW 1 1
2 1N LW 2 2
1
2
LWN
22
1 2
Cr
Solve for .2
Cr C
Copyright 2014 Scott Storla
Oper Inv
2 2
2
Cr
2 r C
1 1 2 2 2Solve q q 1 for L L L
1 1 2 2q q 1L L
Copyright 2014 Scott Storla
2 2
1 1 1 1
Oper Inv
q q
L q L q
1 1 1 1q qL L
2 2 1 1q 1 qL L
2 2q q
1 12
2
1 q
q
LL
P P
Solve e for .rtA P r
e rtA P
Copyright 2014 Scott Storla
Oper Inv
^ ln
t t
e
P P
e rtAP
ln ln e rtAP
ln A rtP
t t
ln AP rt
h h
Solve for .
2
h a bA a
Copyright 2014 Scott Storla
Oper Inv
2 2
b bh h
2
h a bA
2 2
2
h a bA
2A h a b
2Aa b
h
b b
2Ab a
h
0ektA T A 0 0A A
t
0Solve e for .ktA T A k
Copyright 2014 Scott Storla
0 0
Oper Inv
e^ lnt t
A A
T T
0ektA T A T T
0ekt
A T
A
0
ln ln ektA T
A
0ln
A Tkt
A
0ln
A TA
kt
t
a a
Solve aln k b for .y x x
Copyright 2014 Scott Storla
Oper Inv
ln ^k k
ea ab b
lny a x k b
k k
lny b a x k
lny b
x ka
ln
y b
a x ke e
y b
ae x k
y b
ae k x
b b
g g
2 1
.2
Solve h gt for t
Copyright 2014 Scott Storla
12
Oper Inv
^2
2
g g
21
2h gt
212 2
2h gt
22h gt
22ht
g
2ht
g
23 3
3
Vr
h
Copyright 2014 Scott Storla
33
Oper Inv
^2
h h
2
3V r h
2Solve for .3
V r h r
h
3Vr
h
23Vr
h
2
3V r h
h
2
3
Vr
h
Literal EquationsPractice
Copyright 2014 Scott Storla
Copyright 2014 Scott Storla
Solve for .rtA Pe r
2Solve 0 for y. ay bx c
Solve 1 for . ktL A e k
2Solve 1
for .2
h gt g
Solve for .y mx b x
Copyright 2014 Scott Storla
1 2 3 2Solve for .P s s s s
Solve for .2
Cr C
2Solve for .3
V r h h
1Solve for .
2A h a b a
2 1Solve for .
NW N
L
1 1 2 2 2Solve q q 1 for L L L
2Solve 16 50 for .H t t
Solve for .rtA Pe r
1
1Solve for .
y ym y
x x
2Solve 0 for y. ay bx c
0Solve e for k.ktA T A
Solve 1 for . ktL A e k
Solve for .y mx b x
Copyright 2014 Scott Storla
1 2 3 2Solve for .P s s s s
Solve for .2
Cr C
2Solve for .3
V r h h
1Solve for .
2A h a b a
2 1Solve for .
NW N
L
2Solve for .E MC M
2Solve 1
for .2
h gt g