Applying the Properties of Equalities Involving Linear Equations Worksheets

Definition:

In algebra, we always encounter equations specifically linear equation in one variable. The standard form of  this equation is ax + b = c. How do we actually solve the solution to this kind of equation? In this worksheet, you will learn the different properties of equalities of addition, subtraction, multiplication and division that you can apply to solve the equation.

Summary:

Addition Property of Equality states that adding the same number to both sides of two equal expressions will not change the equality of the expressions.

a = b is equivalent to a + c = b + c

Addition Property of Equality states that subtracting the same quantity to both sides of two equal expressions will not change the equality of the expressions.

a = b is equivalent to a - c = b - c

Multiplication Property of Equality states that when we multiply the same quantity to both sides of an equation, the equation remains true.

If a = b, then ac = bc

Division Property of Equality states that when we divide the same quantity to both sides of an equation, the equation remains true.

If a = b and c ≠ 0 then a/c = b/c

Examples:

Solve : x - 8 = 9
Add 8 to both sides
x - 8 + 8 = 9 + 8
x = 17

Solve: x + 19 = 28
Subtract 19 to both sides
x + 19 - 19 = 28 - 19
x = 9