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: Find the Percent Given Two Numbers

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

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

How To: Find a number given Its percent

How To: Do long division without a calculator

How To: Calculate Faster Than a Calculator

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

How To: Find the area of a parallelogram using geometry

How To: Simplify surds (improper square roots)

How To: Calculate percent composition for chemistry

How To: Find the equation of a circle given: center & tangent

How To: Identify characteristics of a sample during a survey

How To: Find the area of a circle when you know the diameter

How To: Solve rational expression simplification word problems

How To: Find the slope of a line given 2 points with fractions

How To: Find the formula of a piecewise function given a graph

How To: Calculate the area of a parallelogram

How To: Find a missing coordinate given: coordinate & equation

How To: Solve percentages without a calculator

How To: Use the ratio formula to find coordinates of a point

How To: Find the Percent Given Two Numbers

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

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

How To: Find a number given Its percent

How To: Do long division without a calculator

How To: Calculate Faster Than a Calculator

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

How To: Find the area of a parallelogram using geometry

How To: Simplify surds (improper square roots)

How To: Calculate percent composition for chemistry

How To: Find the equation of a circle given: center & tangent

How To: Identify characteristics of a sample during a survey

How To: Find the area of a circle when you know the diameter

How To: Solve rational expression simplification word problems

How To: Find the slope of a line given 2 points with fractions

How To: Find the formula of a piecewise function given a graph

How To: Calculate the area of a parallelogram

How To: Find a missing coordinate given: coordinate & equation

How To: Solve percentages without a calculator

How To: Use the ratio formula to find coordinates of a point
Be the First to Comment
Share Your Thoughts