Solving Literal Equations
Solving equations for different variables
-Useful in Physics and MathematicsChapter 3 in Prentice Hall Algebra 1
Review
Solve:
3x + 2 = 8
- 2 -2
3x = 6
÷3 ÷3
x=2
At this level in our mathematics education, we should all
be able to solve this equation. Let’s examine what is
happening in more depth.
3x + 2 = 8
• We are trying to isolate x,
but what is preventing x
from being by itself? Fill in the
Do column, from closest to
x to furthest from x.
Do
Undo
·3
-2
+2
÷3
• Now, fill in the Undo column,
by writing the opposite operations in the
opposite order as the Do column.
• To solve, we simply follow the directions of the
Undo column from top to bottom.
We can follow the same process as we
solve literal equations.
• Solve this common formula for r
d  r t
Do
Undo
·t
÷t
• r is not isolated, because t is multiplying it. Fill in the Do
column.
• Now, fill in the Undo column. What is the opposite
operation of multiplying?
• To solve for r, just follow the directions of the Undo
column.
d  r t
÷t
÷t
d
r
t
We have solved the equation for r, which means
we have isolated r.
Physics Application
• Often, you will be given a formula such as F =
m · a, where F is force, m is mass, and a is
acceleration.
• This works very nicely if you know mass and
acceleration. You can replace m and a with
your known quantities.
• But what if you knew m and F but not a?
When you are working with word
problems, use this format to show
your work and solve:
Givens:
Formula: (and solve for unknown)
Replace formula with givens:
Answer (with proper units):
A 16 g marble is dropped in a cup of water. It has
a volume of 8 cm3. Find its density.
Givens: m = 16 g
v = 8 cm3
d=?
Formula: d = m / v
Replace formula with givens:
d = 16 g / 8 cm3
Answer (with proper units):
d = 2 g/cm3
But what if your formula is not solved for
the variable in question?
Example: A marble is dropped in a cup of water. It has a volume of 8 cm3 and
density of 2 g/cm3. Find its mass.
Givens:
d = 2 g/cm3
v = 8 cm3
m=?
Formula: d = m / v but this is not the formula you need.
Use Do/Undo method to develop a formula to isolate m
m=d·v
Replace formula with givens:
m = 2 g/cm3 · 8 cm3
Answer (with proper units):
m = 16 g
Do
÷v
Undo
·v
Practice Problems
1. What is the mass of a frictionless sled that is
accelerating at 3 meters per second squared
with a force of 130 N? (Use F = m · a)
2. What is the acceleration of a 1000 kg car pulled
by a cable with 2000 N of force? (N = kg·m/s2)
3. How much force is exerted to do 2 J of work in
moving a book 2 m? (W = f · d, Joules = N · m)