Goal: Solve linear equations.

Definitions: Equation: statement in which two expressions are equal. Linear Equation (in one variable): equation that can be written in the form ax = b where a and b are constants and a ≠ 0. Solution (of an equation): if the equation is true when the number is substituted for the variable. Equivalent Equations: equations that have the same solution.

Properties of Equality

Example 1: Solve a One-Step Equation Solve x – 8 = 12 Solve y – 7 = 5

Example 2: Solve a Multi-Step Equation Solve -3x + 6 = -12 Solve -4t + 8 = 40

Example 3: Solve an Equation with Variables on Both Sides Solve 3p + 7 = 5p - 1 Solve 8b – 16 = 13b + 9

Checkpoint: Solve Equations

Example 4: Use the Distributive Property Solve 2(5x – 6) = -4(x – 3) + 4 Solve 4(2x – 9) + 5x = -3 (10 – x)

Example 5: Solve an Equation with Fractions

Checkpoint: Solve Equations