Expressions, Equations, Simplifying, and Solving
There are big differences between expressions and equations, and what we have to do
mathematically depends on which of the two we’re given.
Expressions
Equations
1) An expression has no “=” built into the
problem.
Ex: 4(2x – 7)
1) An equation has an “=” built into the
problem.
Ex: 4(2x – 7) = 3x + 10
2) Cannot “solve for x” or end up with an
answer of “x = ____”
2) Can “solve for x” or end up with an
answer of “x = ____”
3) Based on #2, we can only simplify, not
solve.
3) Based on #2, we can simplify and/or
solve.
4) Therefore, the instructions for
expressions are generally “Simplify the
following”.
4) Therefore, the instructions for
expressions are generally “Solve for the
variable”.
5) We cannot do things to “both sides” of
an expression. An expression doesn’t
have two sides!
5) We can do things to “both sides” of an
equation, i.e. “Add two to both sides”.
6) An equation is really just two
expressions joined together by an “=”
sign.
Sections 1.4 and 2.1 hints that can help eliminate errors.
1. When distributing, work positive/negative signs separately from the numbers.
Example: –4(x + 2)
2. Do “scratch work” off to the side so that the original problem stays organized.
3. Use “walls” when solving equations and moving things from one side to the other.
4. Line one step directly under the previous step.
Section 2.2 hints
1. Identify what we’re solving for.
2. Figure out how everything else on the same side of the = sign is attached to the variable
we’re solving for in step 1.
P
3. Use inverse operations and
R
E
M D
A S
from bottom to top to solve for the wanted variable.