Summary
Highlights
A review of how to add, subtract, multiply, and divide fractions. When adding or subtracting, find a common denominator. When multiplying, multiply across. When dividing, keep the first fraction, change the division to multiplication, and flip the second fraction (keep change flip).
Learn how to add and subtract like terms, where variables and their exponents must be identical. When multiplying variables, add their exponents (e.g., x^4 * x^7 = x^11). When dividing, subtract exponents (e.g., x^7 / x^4 = x^3). When raising an exponent to another power, multiply the exponents (e.g., (x^3)^4 = x^12). Also, any number raised to the power of zero is 1.
Understand how to distribute when multiplying a monomial by a binomial, or how to 'foil' when multiplying two binomials. The FOIL method (First, Outside, Inside, Last) helps multiply terms systematically. Also, demonstrated is multiplying a binomial by a trinomial and a trinomial by a trinomial, suggesting organizing terms vertically for clarity.
Introduction to solving linear equations. The goal is to isolate the variable by performing inverse operations. Examples include equations with addition, subtraction, multiplication, and division. For multi-step equations (e.g., 3x + 5 = 11), isolate the term with the variable first.
Learn to solve equations where variables appear on both sides. Gather all variable terms on one side and constant terms on the other. For equations with parentheses, first distribute to remove them, then proceed with isolating the variable.
Strategies for solving equations containing fractions: multiply the entire equation by the reciprocal of a fractional coefficient, or by the least common multiple of all denominators to eliminate fractions. For equations with decimals, multiply by a power of 10 (10, 100, etc.) to convert decimals into whole numbers.
When two fractions are separated by an equal sign, you can cross-multiply to solve for the variable. This technique simplifies the equation by removing the denominators.
Learn to represent inequalities on a number line: use an open circle for 'greater than' or 'less than', and a closed circle for 'greater than or equal to' or 'less than or equal to'. Shade the appropriate direction. Additionally, understand interval notation for these graphical representations. When solving inequalities, remember to reverse the inequality sign if multiplying or dividing by a negative number.