Solve Multi-Step
Equations
POWER to
the brain.
Solving Equations
Solving and equation to determine the
“unknown” (the variable) is simply working
backward by applying the inverse operation
of how the equation was originally
constructed.
Two-Step Equation (from yesterday)
n – 8 = -5
3
Now, it’s changed into a
Multi-Step Equation
2n – 8 = -6
3
Practice Problem
3n + 6 = -6
5
Simplifying Equations
Before an equation can be solved, the
equation must FIRST BE SIMPLIFIED.
A simplified equation has:
• applied the distributive property if applicable
• all terms are combined
• the unknown variable is only on one side of
the equal sign
Remember solving an
equation is a balancing act
What you do to
one side you
have to do to
the other!!
Combining Like Terms
First…
7 x  3x  8  24
Practice Problem
5x + 3 – 7x – 4 = 15
Practice
1. 5a – 7 + 3a = 17
2. 9b + 6 – 5b = 18
3. -5c – 10 – 5c – 2 = 8
4. 15n + 16n + 4n = 140
Simplify By Using
the Distributive Property
Distributive Property – Multiply what is on the outside
of parentheses by everything in the parentheses.
a(b + c) = ab + ac
OR a(b – c) = ab – ac
Example 1: -3(x + 5)
-3x – 15
Example 2: -7(2a – 4)
-14a + 28
Practice Problem
-2(n - 5) = -2
Simplify and Solve Equations
Example: 3(x – 2) + 4x = 8
SECOND:
Combine like
terms.
Now it’s a
regular 2-step
equation.
FIRST - Use the
Distributive Property to
get rid of the
parentheses.
Simplify and Solve Equations
Example: 3x + 2(2x – 1) = 33
1.Use
Distributive
Property
2. Combine
Like terms
3. Use Inverse
Operations
Practice
1. 4(x + 1) + 5 = 13
2. 5(y + 2) – y = -26
3. -9x + 6(2x + 8) = 96
4. 7y – 2(8y + 1) = 16