Linear Equations and Absolute Value Equations Chapter 8 A Transition Section 1 Linear Equations and Absolute Value Equations

Solving Linear Equations Simplify each side of the equation completely. Use the distributive property to clear any parentheses. If there are fractions in the equation, multiply both sides of the equation by the LCM of the denominators to clear the fractions from the equation. Combine any like terms that are on the same side of the equation. Collect all variable terms on one side of the equation. Collect all constant terms on the other side of the equation. Divide both sides of the equation by the coefficient of the variable term. Check your solution.

Solving Linear Equations Solve

Solving Linear Equations Solve

Solving Linear Equations Solve

Solving Linear Equations Solve LCM: 12

Contradictions A contradiction is an equation that has no solution, so its solution set is the empty set { }. The empty set is also known as the null set, and is denoted by the symbol

Contradictions Solve

Identities An identity is an equation that is always true. The solution set for an identity is the set of all real numbers, denoted . An identity has infinitely many solutions.

Identities Solve

Solving Absolute Value Equations For any expression X and any positive number a, the solutions to the equation can be found by solving the two equations and

Solve |x| = 6. The absolute value of a number is a measure of the distance between 0 and that number on a real number line. We are looking for a number that is 6 units away from zero. The solution set is {–6, 6}.

Solving Absolute Value Equations Solve: or

Solving Absolute Value Equations Solve: An absolute value is nonnegative, so the equation has no solution:

Solving Absolute Value Equations Involving Two Absolute Values For any expressions X and Y, the solutions to the equation can be found by solving the two equations and

Solving Absolute Value Equations Involving Two Absolute Values Solve: or