Download Expressions and Equations Review Sheet

Expressions and Equations Review Sheet
Combining Like Terms:
Like terms have the same variable raised to the same power.
We can only add or subtract like terms. We cannot add or subtract unlike terms.
Example: 5x + 3y + 6x +2y = 11x + 5y
Note: When there is subtraction in an expression, you should change it to addition to prevent
mistakes.
Example: 3x + 2y – 2x – y = 3x + 2y + (-2x) + (-y) = x + y
Distributive Property: a(b+c) = a(b) + a(c)
We use the distributive property when we are multiplying a number by unlike terms in
parentheses
Example: 6(2x+3) = 6(2x) + 6(3) = 12x +18
Simplifying Algebraic Expressions
Step 1: Change addition to subtraction
Step 2: Distribute
Step 3: Combine like terms.
Example: 2 + 3(x-5) + 3x
2+3(x+ (-5)) + 3x Change subtraction to addition
2+3x-15+3x
Distribute
6x-13
Combine like terms
Inverse Operations: Inverse operations are used to undo operations in equations.
Addition and Subtraction are inverses of each other.
Multiplication and Division are inverses of each other.
The inverse of a fraction is its reciprocal (the flip of the fraction).
One Step Equations:
Step 1: Identify the variable.
Step 2: Identify the operation that is being done to the variable.
Step 3: Perform the inverse operation.
Step 4: Check your answer by plugging the answer back into the equation.
Note: 4x is multiplication;
𝑥
4
is division
Example: x+5=17
-5 -5 Subtract 5 from both sides
x = 12
Two Step Equations
Solve equations by undoing operations in the opposite order of PEMDAS.
Step 1: Identify the variable.
Step 2: Identify any addition or subtraction that is being done to the variable.
Step 3: Perform the inverse operation.
Step 4: Identify any multiplication or division that is being done to the variable.
Step 5: Perform the inverse operation.
Step 6: Check your answer by plugging it back into the equation.
Example: 5x + 8 = 28
-8
-8
Subtract 8
5x=20
x=4
Divide by 5
Multi Step Equations
Step 1: Simplify both sides of the equation by distributing and combining like terms.
Step 2: Solve the equation the same way you would solve a two step equation.
Distributing Fractions in Equations
Method One: Multiply both sides by the reciprocal.
Method Two: Multiply both sides by the least common denominator.
Note: You must always get rid of anything being adding or subtracted to the variable before
multiplying by the reciprocal or LCD.
Translating Words to Expressions:
Break apart the words to write them as a mathematical expression.
Less than: switch the order of the numbers
Subtracted from: switch the order of the numbers
Algebraic Equations (word problems):
Step 1: Identify the variable.
Step 2: Write an equation.
Step 3: Solve and check.
Step 4: Label your answer