Solving Linear Equations Using the Addition Property of Equality

Equations, Inequalities, and Problem Solving

Solving Linear Equations

Solving linear equations is a fundamental skill in intermediate algebra. The goal is to isolate the variable on one side of the equation using properties of equality, such as the addition property.

• Linear Equation: An equation of the form ax + b = c, where a, b, and c are constants.

• Addition Property of Equality: If you add (or subtract) the same number to both sides of an equation, the equality is maintained.

Example: Solve and Check

Consider the equation:

$-13 = x + 15$

• Step 1: Isolate the variable. Subtract 15 from both sides to move all variable terms to one side and constants to the other:

$-13 - 15 = x + 15 - 15$

$-28 = x$

• Step 2: Check the solution. Substitute x = -28 back into the original equation:

$-13 = (-28) + 15$

$-13 = -13$

• Since the statement is true, -28 is the solution.

• Solution Set: { -28 }

Key Points

• Always perform the same operation on both sides of the equation to maintain equality.

• Check your solution by substituting the value back into the original equation.

• The solution set is written using curly braces, e.g., { -28 }.