literal equations

1. Literal Equations

2. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation.
Literal Equations

3. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation.
Literal Equations
Example A.
a. Solve for x if x + b = c
b. Solve for w if yw = 5.

4. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We try to accomplish this just as solving equations
for the x, by +, – the same term, or * , / by the same quantity
to both sides of the equations.
Example A.
a. Solve for x if x + b = c
Literal Equations
b. Solve for w if yw = 5.

5. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We try to accomplish this just as solving equations
for the x, by +, – the same term, or * , / by the same quantity
to both sides of the equations.
Example A.
a. Solve for x if x + b = c
Remove b from the LHS by subtracting from both sides
x + b = c
–b –b
x = c – b
Literal Equations
b. Solve for w if yw = 5.

6. Example A.
a. Solve for x if x + b = c
Remove b from the LHS by subtracting from both sides
x + b = c
–b –b
x = c – b
Literal Equations
b. Solve for w if yw = 5.
Remove y from the LHS by dividing both sides by y.
Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We try to accomplish this just as solving equations
for the x, by +, – the same term, or * , / by the same quantity
to both sides of the equations.

7. Example A.
a. Solve for x if x + b = c
Remove b from the LHS by subtracting from both sides
x + b = c
–b –b
x = c – b
Literal Equations
b. Solve for w if yw = 5.
Remove y from the LHS by dividing both sides by y.
yw = 5
yw/y = 5/y
Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We try to accomplish this just as solving equations
for the x, by +, – the same term, or * , / by the same quantity
to both sides of the equations.

8. Example A.
a. Solve for x if x + b = c
Remove b from the LHS by subtracting from both sides
x + b = c
–b –b
x = c – b
5
y
Literal Equations
b. Solve for w if yw = 5.
Remove y from the LHS by dividing both sides by y.
yw = 5
yw/y = 5/y
w =
Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We try to accomplish this just as solving equations
for the x, by +, – the same term, or * , / by the same quantity
to both sides of the equations.

9. Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

10. To solve for a specific variable in a simple literal equation, do
the following steps.
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

11. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

12. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

13. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for – move all the other terms to other side of the
equation.
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

14. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for – move all the other terms to other side of the
equation.
3. Isolate the specific variable by dividing the rest of the
factor to the other side.
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

15. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for – move all the other terms to other side of the
equation.
3. Isolate the specific variable by dividing the rest of the
factor to the other side.
Literal Equations
Example B.
a. Solve for x if (a + b)x = c
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

16. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for – move all the other terms to other side of the
equation.
3. Isolate the specific variable by dividing the rest of the
factor to the other side.
Literal Equations
Example B.
a. Solve for x if (a + b)x = c
(a + b) x = c div the RHS by (a + b)
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

17. To solve for a specific variable in a simple literal equation, do
the following steps.
1. If there are fractions in the equations, multiple by the
LCD to clear the fractions.
2. Isolate the term containing the variable we wanted to
solve for – move all the other terms to other side of the
equation.
3. Isolate the specific variable by dividing the rest of the
factor to the other side.
Literal Equations
Example B.
a. Solve for x if (a + b)x = c
(a + b) x = c
x =
c
(a + b)
div the RHS by (a + b)
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

18. b. Solve for w if 3y2w = t – 3
Literal Equations

19. b. Solve for w if 3y2w = t – 3
3y2w = t – 3 div the RHS by 3y2
Literal Equations

20. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
w =
t – 3
3y2
div the RHS by 3y2
Literal Equations

21. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
w =
t – 3
3y2
div the RHS by 3y2
Literal Equations

22. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
w =
t – 3
3y2
div the RHS by 3y2
move b2 to the RHS
Literal Equations

23. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
div the RHS by 3y2
move b2 to the RHS
Literal Equations

24. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations

25. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations

26. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10

27. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand

28. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand
ax – ay = 10

29. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand
ax – ay = 10 subtract ax

30. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand
ax – ay = 10 subtract ax
– ay = 10 – ax

31. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand
ax – ay = 10 subtract ax
– ay = 10 – ax div by –a

32. b. Solve for w if 3y2w = t – 3
3y2w = t – 3
c. Solve for a if b2 – 4ac = 5
b2 – 4ac = 5
– 4ca = 5 – b2
w =
t – 3
3y2
a = 5 – b2
–4c
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations
d. Solve for y if a(x – y) = 10
a(x – y) = 10 expand
ax – ay = 10 subtract ax
– ay = 10 – ax div by –a
y =
10 – ax
–a

33. Multiply by the LCD to get rid of the denominator then solve.
Literal Equations

34. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
Example C.
Solve for d if
Literal Equations

35. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d– 4 = d
3d + b
Example C.
Solve for d if
Literal Equations

36. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 = d
3d + b
( )
d
Example C.
Solve for d if
Literal Equations

37. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
Example C.
Solve for d if
Literal Equations

38. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
– 4d = 3d + b
Example C.
Solve for d if
Literal Equations

39. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
– 4d = 3d + b move –4d and b
Example C.
Solve for d if
Literal Equations

40. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
– 4d = 3d + b
– b = 3d + 4d
move –4d and b
Example C.
Solve for d if
Literal Equations

41. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
– 4d = 3d + b
– b = 3d + 4d
move –4d and b
– b = 7d
Example C.
Solve for d if
Literal Equations

42. –4 =
d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
multiply by the LCD d
d
– 4 = d
3d + b
– 4 =
d
3d + b
( )
d
– 4d = 3d + b
– b = 3d + 4d
move –4d and b
– b = 7d
= d
7
–b
Example C.
Solve for d if
Literal Equations
div. by 7

43. Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation.
Literal Equations
x = 3 +
1
2y
Example D.
Solve for y if

44. Flipping Equations
Literal Equations

45. Flipping Equations
Literal Equations
x = 3 +
1
2y
Example D.
Solve for y if

46. Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation.
Literal Equations
x = 3 +
1
2y
Example D.
Solve for y if

47. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
Literal Equations
B
A
=
C
D
A
B
Reciprocate
both sides
x = 3 +
1
2y
Example D.
Solve for y if

48. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
x = 3 +
1
2y
Example D.
Solve for y if
Literal Equations
B
A
=
C
D
A
B
x = 3 +
1
2y
Reciprocate
both sides

49. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
x = 3 +
1
2y
Example D.
Solve for y if
Literal Equations
B
A
=
C
D
A
B
x = 3 +
1
2y
x – 3 =
1
2y
Reciprocate
both sides

50. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
x = 3 +
1
2y
Example D.
Solve for y if
Literal Equations
B
A
=
C
D
A
B
x = 3 +
1
2y
x – 3 =
1
2y
reciprocating both sides,
= 1
2y
x – 3
1
Reciprocate
both sides

51. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
x = 3 +
1
2y
Example D.
Solve for y if
Literal Equations
B
A
=
C
D
A
B
x = 3 +
1
2y
x – 3 =
1
2y
reciprocating both sides, then div. by 2
= 1
2y
x – 3
1
=
2y
2(x – 3)
1
Reciprocate
both sides
2

52. =
D
C
Flipping Equations
If it’s advantageous to do so,
we may reposition the equation
by reciprocating both sides of
an equation. In particular:
x = 3 +
1
2y
Example D.
Solve for y if
Literal Equations
B
A
=
C
D
A
B
x = 3 +
1
2y
x – 3 =
1
2y
reciprocating both sides, then div. by 2
= 1
2y
x – 3
1
=
2y
2(x – 3)
1
Reciprocate
both sides
2 = y or
2(x – 3)
1
y =

53. Exercise. Solve for the indicated variables.
Literal Equations
1. a – b = d – e for b. 2. a – b = d – e for e.
3. 2*b + d = e for b. 4. a*b + d = e for b.
5. (2 + a)*b + d = e for b. 6. 2L + 2W = P for W
7. (3x + 6)y = 5 for y 8. 3x + 6y = 5 for y
w = t – 3
613. for t w = t – b
a14. for t
w =11. for t w =12. for t
t
6
6
t
w =
3t – b
a15. for t 16. (3x + 6)y = 5 for x
w = t – 3
6
17. + a for t w = at – b
5
18. for t
w =
at – b
c
19. + d for t 3 =
4t – b
t
20. for t
9. 3x + 6xy = 5 for y 10. 3x – (x + 6)y = 5z for y