**Objectives**

- Isolate variables in an equation by using addition or subtraction.
- Solve equations involving addition or subtraction by mapping them on the number line.
- Explain each step in solving an equation using addition or subtraction.
- Ask the questions necessary to turn real-life problems into mathematical sentences.

**Key Terms**

- Isolate the Variable – to get the variable alone on one side of an equation or inequality.
- Reverse Operations – Opposite operations. Reverse operations undo each other. Ex. x + 4 would be x – 4. Addition & subtraction are opposites. Multiplication and division are opposites. Squares and square roots are opposites.

**Notes**

- Standard form of equations:
- Addition: x + a = b
- Has 1 variable (x) and 2 constants (a & b)
- ex. x + 3 = 7

- Subtraction: x – a = b
- Has 1 variable (x) and 2 constants (a & b)
- ex. x – 5 = 6

- Addition: x + a = b

- To solve, you MUST isolate the variable
- Step 1: Determine the operations used in the expression (on the same side of the equation as the variable)
- ex. x + 4 = 10 (+ is the operation used in the expression x + 4, which is on the LEFT side of the equation)

- Step 2: Perform the inverse (or REVERSE) operation
- If you have positive / addition, then you must subtract
- If you have negative / subtraction, then you must add
- Whatever you do to one side of the equation, you MUST do to the other side
- BOTH sides of the equation must be balanced

- Step 3: Perform any additional reverse operations on other constants or coefficients
- Step 4: Write your answer in terms of a positive variable solution (you may have to divide by -1 on both sides)
- ex. -x = 4 (divide by -1 on both sides to get: x = -4)
- ex. g = -6 (already in proper solution form with a positive variable)
- ex. -b = -100 (divide by -1 on both sides to get b = 100)
- Note: sometimes problems are not in standard form (ex. 4 = 3 – x), so you have a choice:
- 1. Put them problem in standard form: (3 – x = 4 ==> -x + 3 = 4)
- 2. Solve as is, using reverse operations (subtract the 3 on both sides, THEN divide by -1 on both sides to get -1 = x)
- Remember: -1 = x is the exact same thing as x = -1

- Step 1: Determine the operations used in the expression (on the same side of the equation as the variable)