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Absolute Value

What is a number's ABSOLUTE VALUE? The absolute value of a number is it's distance from zero, (when plotted on a number line.)
When solving an absolute value equation, first you must always ISOLATE the absolute value.
An absolute value expression must always be a non-negative number. It can equal zero, or any positive.
How do you ISOLATE an absolute value? Move all other terms to the other side of the equal, or inequality sign.
Absolute Value Equation Form |X| = a |X| represents an expression containing a variable, (in this case equal to a.) Is a is a positive number, then |X| = a is equivalent to X = a and X = -a. If a = 0, then solve so that X = 0.
Absolute Value Equation Form |X| = |Y| |X| and |Y| are two separate expressions both containing a variable. X = Y and X = -Y
Absolute Value Inequality Form |X| < a In a Less Than Inequality you use a COMPOUND INEQUALITY to solve. -a < X < a When solving, all three terms must be treated equally.
Absolute Value Inequality Form |X| > a IN a GREATER THAN Inequality you set up TWO DISJOINT LINEAR INEQUALITIES to solve. X < -a or X > a
What must you do to the inequality symbol(s) when multiplying or dividing both sides of an inequality by a NEGATIVE number? REVERSE the inequality symbol.
Absolute Value Inequality Form |x| < a or |x| > a |x| represents a variable that is "a" distance from zero.
Created by: CoryBrydges