# 1.5 – Solving with Addition and Subtraction

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

• 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