Lesson 2: Solving Equations Using Addition or Subtraction

Property

An equation is a question asking of two expressions: for what values of the unknowns do the expressions give the same result. Those values are called the solutions.
Two equations are equivalent if they have the same solution set.

Examples

Property

Addition and subtraction are inverse operations that undo each other: $a + b - b = a$ and $a - b + b = a$

Properties of Equality maintain balance:

• Addition Property: If $a = b$, then $a + c = b + c$
• Subtraction Property: If $a = b$, then $a - c = b - c$

Property

To solve equations, we apply the rules of equivalence to isolate the variable.
For equations in the form $x + p = q$, we find the solution by subtracting $p$ from both sides.
For equations in the form $x - p = q$, we find the solution by adding $p$ to both sides. All numbers $p$, $q$, and $x$ are rational numbers.

Examples