Introduction to Algebra

Vocabulary

• Variable –
• Coefficient –
• Expression –
• Equation –
• Term –

Signed Numbers

• Addition and Subtraction
• Adding positive numbers moves to the right on the number line
• Subtracting positive numbers moves to the left on the number line
• Adding negative numbers moves to the left on the number line
• Subtracting negative numbers moves to the right on the number line
• Notice: subtracting a negative number is like adding a positive number
• To add mixed numbers, ignore signs and subtract the smaller from the larger, then add the sign of the larger.
• Multiplication and Division – multiply or divide normally, ignoring signs, then determine the sign of the result using the following table (A*B or A/B):

A	B	Sign of Result
+	+	+
+	-	-
-	+	-
-	-	+

Combining Like Terms

• Addition – increase the coefficient of the variables (Subtraction – decrease the coefficient)

Example: 5x + 3x

The five and the three add together to make eight x’s (equals 8x).

• Multiplication – multiply any coefficients, and increase the exponent of the variable
  (Division – divide any coefficients, decrease the exponent of the variable)

Example: (5x)(3x) = 15x²

Order of Operations

Use the mnemonic phrase “Please Excuse My Dear Aunt Sally” to remember to solve in this order:

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

Evaluating Expressions

Substitute the given value for the variable in the expression, and solve for a final numerical value.

Evaluating Equations

Isolate a single variable on one side of the equation and a numerical value on the other.

Example: 3x + 4 = x - 6

3x + 4 - 4 = x – 6 - 4

3x = x – 10

3x - x = x - x – 10

2x = – 10

(2x) ÷ 2 = (– 10) ÷ 2

x = – 5