Absolute Value
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| 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.)
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| When solving an absolute value equation, first you must always | ISOLATE the absolute value.
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| An absolute value expression must always be a non-negative number. | It can equal zero, or any positive.
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| How do you ISOLATE an absolute value? | Move all other terms to the other side of the equal, or inequality sign.
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| 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.
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| Absolute Value Equation Form |X| = |Y| | |X| and |Y| are two separate expressions both containing a variable.
X = Y and X = -Y
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| 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.
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| 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
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| 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.
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| Absolute Value Inequality Form |x| < a or |x| > a | |x| represents a variable that is "a" distance from zero.
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Created by:
CoryBrydges
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