Study Guide
One-Step; Two-Step; Distributive Property;
Combining Like Terms
Solving One-Step Equations:
Step One: Whatever you do to one side of the equation you must do to the
other side.
Step Two: In order to solve for x, we must isolate (get all by its lonesome
self) the variable. The most straightforward way to get a variable alone is
to undo the operation that accompanies it.
Subtraction is the opposite of Addition
𝑥 − 4 = 13
+4
+4
𝑥 = 19
𝑥 + 12 = 45
-12
-12
𝑥 = 33
Division is the opposite of Multiplication
2
2𝑥 = 40
(5) 𝑥 = 12(5)
÷2
2𝑥 = 60
÷2
𝑥 = 20
5
𝑥 = 60
Step Three: Check - Plug your answer back into the original equation to
see if it works.
Solving Two-Step Equations:
Step 1: Combine Like Terms
Step 2: Isolate the terms that contain the variable you wish to solve for.
Step 3: Isolate the variable you wish to solve for.
Step 4: Substitute your answer into the original equation and check that it
works.
Study Guide
One-Step; Two-Step; Distributive Property;
Combining Like Terms
Distributive Property:
Distribute means to GIVE.
When you use the distributive property, you are GIVING the
number/variable on the outside of the parenthesis to the numbers/variables
on the inside of the parenthesis.
GIVING = MULTIPLICATION
Step 1: Draw the arrows to the terms that are being distributed to. Each
arrow represents multiplication.
Step 2: Multiply.
Step 3: Simplify if possible by combining like terms.
Combining Like Terms:
When solving problems with multiple terms and variables, we can combine
“common” terms to make the problem simpler.
To be a common term, the term must have the same variable and the same
exponents.
When you have a variable that does not have a coefficient, you may write
in a 1 to help you.
Step 1: Organize your like terms. You can use a highlighter, shapes, or just
rewrite the problem so that the like terms are next to each other.
Step 2: Combine the coefficients.
Study Guide
One-Step; Two-Step; Distributive Property;
Combining Like Terms
Solving Multi-Step Equations – Distributive Property
To solve a multi-step equation:
1. Perform any distributive property shown in the equation.
2. Combine any like terms in the equation (do not cross the = sign)
3. Now you should see a two-step equation remaining, please follow the
steps for solving two step equations.
To solve an equation with variables on both sides:
1. Perform any distributive property shown in the equation.
2. Combine any like terms in the equation (do not cross the =).
3. Move variable terms to one side of the equation, and constants to the
other side of the equation.
a. It doesn’t matter to which side you choose to move things.
b. Continue using inverse operations to move things properly.