53
Literal Equations
| Date post: | 22-Jan-2018 |
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Literal Equations
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
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.
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.
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.
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.
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.
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
5y
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.
Literal EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
To solve for a specific variable in a simple literal equation, do
the following steps.
Literal EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
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 EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
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 EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
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 EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
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 EquationsAdding or subtracting a term to both sides may be viewed as
moving the term across the " = " and change its sign.
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.
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.
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.
b. Solve for w if 3y2w = t – 3
Literal Equations
b. Solve for w if 3y2w = t – 3
3y2w = t – 3 div the RHS by 3y2
Literal Equations
b. Solve for w if 3y2w = t – 3
3y2w = t – 3
w =t – 3 3y2
div the RHS by 3y2
Literal Equations
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
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
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
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
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
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
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
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
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
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
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
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
Multiply by the LCD to get rid of the denominator then solve.
Literal Equations
–4 =d
3d + b
Multiply by the LCD to get rid of the denominator then solve.
Example C.
Solve for d if
Literal Equations
–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
–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 = d3d + b
( )d
Example C.
Solve for d if
Literal Equations
–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
–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
–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
–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
–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
–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
= d7
–b
Example C.
Solve for d if
Literal Equations
div. by 7
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 +12y
Example D.
Solve for y if
Flipping Equations
Literal Equations
Flipping Equations
Literal Equations
x = 3 +12y
Example D.
Solve for y if
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 +12y
Example D.
Solve for y if
=DC
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
BA
=CD
AB
Reciprocate
both sides
x = 3 +12y
Example D.
Solve for y if
=DC
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 +12y
Example D.
Solve for y if
Literal Equations
BA
=CD
AB
x = 3 +12y
Reciprocate
both sides
=DC
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 +12y
Example D.
Solve for y if
Literal Equations
BA
=CD
AB
x = 3 +12y
x – 3 =12y
Reciprocate
both sides
=DC
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 +12y
Example D.
Solve for y if
Literal Equations
BA
=CD
AB
x = 3 +12y
x – 3 =12y
reciprocating both sides,
=12y
x – 31
Reciprocate
both sides
=DC
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 +12y
Example D.
Solve for y if
Literal Equations
BA
=CD
AB
x = 3 +12y
x – 3 =12y
reciprocating both sides, then div. by 2
=12y
x – 31
=2y
2(x – 3)1
Reciprocate
both sides
2
=DC
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 +12y
Example D.
Solve for y if
Literal Equations
BA
=CD
AB
x = 3 +12y
x – 3 =12y
reciprocating both sides, then div. by 2
=12y
x – 31
=2y
2(x – 3)1
Reciprocate
both sides
2= y or
2(x – 3)1
y =
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 a
14. for t
w =11. for t w =12. for tt6
6t
w =3t – b
a15. for t 16. (3x + 6)y = 5 for x
w =t – 3
617. + a for t w =
at – b 5
18. for t
w =at – b
c19. + d for t 3 =
4t – b t
20. for t
9. 3x + 6xy = 5 for y 10. 3x – (x + 6)y = 5z for y
