Equations in One Variable

Lesson Overview

Objective: Understand how to solve problems using simple equations in one variable.
Focus: Writing and solving 2-step equations and absolute value equations.

Absolute Value: The distance of a number from zero on the number line, regardless of direction.
Equation: A mathematical statement that asserts the equality of two expressions.
Identity Property of Addition: Adding zero to a number does not change the number (e.g., a + 0 = a).
Identity Property of Multiplication: Multiplying a number by one does not change the number (e.g., a × 1 = a).
Inverse Operations: Operations that undo each other (e.g., addition and subtraction, multiplication and division).
Properties of Equality: Rules that allow you to manipulate equations, such as adding, subtracting, multiplying, or dividing both sides by the same value without changing the equality.

Example Problem: 1/3 x = -2
Step-by-Step Solution:
- Multiply Both Sides: Instead of dividing by 1/3, multiply both sides by 3 (using the multiplication property of equality).
  - Equation becomes: x = -6
Identity Property:
- After multiplication, we have 1x, which is equivalent to x, hence x = -6.
Check the Solution: Substitute -6 back into the original equation:
- Calculate: 1/3 * (-6) = -2.
- This confirms that the solution is correct as it satisfies the original equation.

Next Steps: Engage in practice problems using the concepts of writing and solving equations to enforce understanding and application.