MAT 112: Linear Equations, Inequalities, and Absolute Value Overview

This module provides a foundational review of essential algebraic concepts, starting with basic vocabulary and progressing through solving various types of equations and inequalities.

I. Fundamental Vocabulary and Operations

The module begins by defining factors as numbers or variables that multiply to produce another number, noting they are finite and typically listed in increasing or alphabetical order. Multiples are introduced as the product of a number and any whole number, emphasizing their infinite nature. The concept of the Least Common Multiple (LCM), also known as the Least Common Denominator (LCD), is explained with two strategies: listing multiples or using prime factorization to find the highest exponent of each factor.

The Order of Operations, commonly remembered by the acronym PEMDAS, is reviewed: Parentheses/Grouping symbols, Exponents, Multiply/Divide (from left to right), and Add/Subtract (from left to right). This sequence ensures consistent evaluation of mathematical expressions.

II. Fractions Review

A comprehensive review of fraction operations is provided, covering simplifying fractions by dividing out common factors, multiplying fractions by multiplying numerators and denominators, and dividing fractions by multiplying by the reciprocal of the second fraction. For adding and subtracting fractions, the crucial step of finding a common denominator (often the LCM) is highlighted before combining the numerators.

III. Solving Linear Equations

The core goal of solving equations is to isolate the variable on one side of the equals sign. This is achieved by applying inverse operations equally to both sides of the equation. The process typically involves distributing terms, collecting like terms, and, for equations with fractions, clearing them by multiplying all terms by the Least Common Denominator (LCD).

IV. Inequalities

Inequalities are introduced with their symbols, where the