Literal Equations An Introduction Copyright 2014 Scott Storla

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.


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.


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.


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


Operation Inverse

22L 2L

2

2

2

P LW

Literal EquationsAn Introduction


Literal EquationsPractice


m my b mx

b b

Solve for .y mx b x

y mx b


Oper Inv

m m

b b

y bx

m

2 1

1

L NLW

L

2 1Solve for .

NW N

L

2 1NW

L


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


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


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


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


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


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


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


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


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



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


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


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

Documents

Literal Equations An Introduction Copyright 2014 Scott Storla