Solving Literal
Equations:
Solving literal equations
(formulas) for a
specified variable.
Definitions
An equation is a mathematical sentence
that contains an equal sign ( = ).
Ex: x = yz What do x, y, and z stand
for?
A formula is an equation that states a rule
for the relationship between certain
quantities.
Ex: A = lw What do A, l, and w stand
for?
What does it mean to
solve:
To solve for x would mean to get x by
itself on one side of the equation, with
no x’s on the other side. (x = __ )
Similarly, to solve for y would mean to
get y by itself on one side of the
equation, with no y’s on the other side.
(y = __ )
1) Solve 2a - 4d = 7 for x
To get x by itself, what is the first step?
1. Add 2a
2. Subtract 2a
3. Add 4d
4. Subtract 4d
Answer Now
2) Solve 2a - 4d = 7 for d
What is the first thing we are doing to d?
What is the second thing?
Undo add 2a to both sides by subtracting 2a
on both sides
Undo multiply by -4 to both sides by dividing
by -4 on both sides
Follow the steps in
reverse (UNDO) to
isolate the variable.
1) Solve 2a - 4d = 7 for x
+4d + 4d
2a = 7 + 4d
1. Add 4y to both 2
2
sides
2. Simplify
7  4d
a
3. Divide both sides by
2
2
4. Does it simplify?
This fraction cannot be
simplified because both terms
in the numerator are not
divisible by 2.
2) Solve 2x - 4y = 7 for y
To get y by itself, what is the first
step?
1. Add 2x
2. Subtract 2x
3. Add 4y
4. Subtract 4y
Answer Now
2) Solve 2x - 4y = 7 for y
-2x
- 2x
-4y = 7 - 2x
-4
-4
1. Subtract 2x from
both sides
2. Simplify
3. Divide both sides by
-4
4. Does it simplify?
Nope!
7  2x
y
4
ya
3) Solve
 c for y.
3
What is the first step?
1. Multiply by 3
2. Divide by 3
3. Add a
4. Subtract a
Answer Now
y

a
3) Solve for y:
c
3
ya
3
c 3
3
1. Clear the fraction –
Multiply both sides by
y + a = 3c
3
2. Simplify
-a -a
3. Subtract a from both
y = 3c - a
sides
4. Simplify
4) Solve for y: 4x – 2y = 12
1. -4x + 12
2. 4x - 12
3. -2x + 6
4. 2x - 6
Answer Now
4) Solve for y: 4x – 2y = 12
- 4x
- 4x
-2y = 12 – 4x
-2
-2
Subtract 4x from both sides
Simplify
Divide both sides by -2
Does it simplify?
Yes!
y = -6 + 2x
5) The formula for the volume of a
rectangular prism is V = LWH. Which
equation solves the formula for L?
1.
L = V - WH
2. L V H
W
3. L V W
H
4. L  V
HW
Answer Now
6) The formula for the volume of a
1
pyramid is V = 3 bh . Which equation
solves the formula for h?
1.
h = 3Vb
3b
2. h 
V
3. h  3V
b
4. h  V
3b
Answer Now