View the absolute value of a number as its distance from zero. When you take the absolute value of a number, you always end up with a positive number (or zero). Whether the input was positive or negative (or zero), the output is always positive (or zero). For instance,  3  = 3, and  _3  = 3 also. This property that both the positive and the negative become positive makes solving absolutevalue equations a little tricky. But once you learn the "trick", they're not so bad. Let's start with something simple: Solve  x  = 3 This is already solved:  3  = 3 and  _3  = 3, so x must be 3 or _3. But how are you supposed to solve this if you don't already know the answer? You use the positive/negative property of the absolute value to split the equation into two cases, and you use the fact that the minus sign " _ " indicates "the opposite sign", not necessarily a negative number. For example, if you have x = _6, then " _x " indicates "the opposite of x", or, in this case, _(_6) = +6, a positive number. The minus sign in " _x " just indicates that you are changing the sign on x. It does not indicate a negative number. This distinction can be crucial. Whatever the value of x might be, taking the absolute value of x makes it positive. Since x might have been positive and might have been negative, you have to acknowledge this fact when you take the absolutevalue bars off, and you do this by splitting the equation into two cases. If the value of x was positive to start with, then you can bring that value out of the absolutevalue bars without changing its sign, giving you x = 3. But x might also have been negative, in which case you would have to change the sign on x for the absolute value to come out positive, so you also have _x = 3, which solves as x = _3. Then the solution is x = _3, 3.
 Hot
 Latest

How To: Use ">" (greater than) and "<" (less than) symbols

How To: Remember "greater than" & "less than" symbols

How To: Divide small numbers by big numbers

How To: Convert between diameter and radius

How To: Solve a line integral over a closed path

How To: Find a missing side of a triangle, similar to another

How To: Draw a rectangle

How To: Find the area & perimeter of triangles & squares

How To: Use a TI89 to calculate nCr

How To: Divide decimals

How To: Do long division with decimals

How To: Find the equation of an ellipse given a graph

How To: Calculate Faster Than a Calculator

How To: Calculate percent composition for chemistry

How To: Find the 100th term in a sequence

How To: Find the Slope Given 2 Ordered Pairs

How To: Find the slope from a set of points

How To: Figure out the domain & range of a piecewise function

How To: Factor a trinomial with negative leading coefficient

How To: Divide and give an answer as a fraction

How To: Use ">" (greater than) and "<" (less than) symbols

How To: Remember "greater than" & "less than" symbols

How To: Divide small numbers by big numbers

How To: Convert between diameter and radius

How To: Solve a line integral over a closed path

How To: Find a missing side of a triangle, similar to another

How To: Draw a rectangle

How To: Find the area & perimeter of triangles & squares

How To: Use a TI89 to calculate nCr

How To: Divide decimals

How To: Do long division with decimals

How To: Find the equation of an ellipse given a graph

How To: Calculate Faster Than a Calculator

How To: Calculate percent composition for chemistry

How To: Find the 100th term in a sequence

How To: Find the Slope Given 2 Ordered Pairs

How To: Find the slope from a set of points

How To: Figure out the domain & range of a piecewise function

How To: Factor a trinomial with negative leading coefficient

How To: Divide and give an answer as a fraction
Be the First to Comment
Share Your Thoughts