literal equations

1. Literal Equations
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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. We do this, just as solving equations in x,
Literal Equations

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 do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
Literal Equations

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 do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
Literal Equations

6. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
Example A.
a. Solve for x if x + b = c
Literal Equations

7. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
Example A.
a. Solve for x if x + b = c
Remove b from the LHS by subtracting from both sides
x + b = c
Literal Equations

8. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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
Literal Equations

9. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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

10. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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
b. Solve for w if yw = 5.
Literal Equations

11. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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
b. Solve for w if yw = 5.
Remove y from the LHS by dividing both sides by y.
yw = 5
Literal Equations

12. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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
b. Solve for w if yw = 5.
Remove y from the LHS by dividing both sides by y.
yw = 5
yw/y = 5/y
Literal Equations

13. Given an equation with many variables, to solve for a particular
variable means to isolate that variable to one side of the
equation. We do this, just as solving equations in x, by
+, –, * , / the same quantities to both sides of the equations.
These quantities may be numbers or variables.
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
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 = 5
y
Literal Equations

14. 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.
Literal Equations
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.
Literal Equations
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
Literal Equations
Adding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.

18. 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.

19. 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.

20. 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.

21. 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.

22. 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.

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

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

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

26. 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

27. 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

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
div the RHS by 3y2
move b2 to the RHS
Literal Equations

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
div the RHS by 3y2
move b2 to the RHS
div the RHS by –4c
Literal Equations

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

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

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

33. 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

34. 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

35. 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

36. 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

37. 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

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

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

43. –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

44. –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

45. –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

46. –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

47. –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

48. 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