Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Algebra
1. Solves one-variable linear equations and inequalities
Linear equations involve expressions of degree one, where the variable is raised only to the first power. Solving these requires isolating the variable by applying inverse operations.
Steps:
- Simplify each side (remove parentheses using distributive property, combine like terms).
- Move variables to one side and constants to the other.
- Solve for the unknown by division or multiplication.
- Check the solution in the original equation.
Example: 3(2x – 5) – 4 = 2(x + 7) → 6x – 15 – 4 = 2x + 14 → 6x – 19 = 2x + 14 → 4x = 33 → x = 33/4
For inequalities, the same steps apply, but if both sides are multiplied or divided by a negative number, the inequality symbol must be reversed.