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When you take the absolute value of a number, the result is always positive, even if the number itself is negative. For a random number x, both the following equations are true: This means that any equation that has an absolute value in it has two possible solutions.

If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.

Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets.

To solve this, you have to set up two equalities and solve each separately. Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: Sciencing Video Vault 1.

This is solution for equation 1. This is the solution for equation 2. Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true.

Absolute value inequalities word problem (video) | Khan Academy |
Writing inequalities algebra Absolute value inequalities Video transcript A carpenter is using a lathe to shape the final leg of a hand-crafted table. A lathe is this carpentry tool that spins things around, and so it can be used to make things that are, I guess you could say, almost cylindrical in shape, like a leg for a table or something like that. |

Solving absolute value inequalities |
Absolute value inequalities Video transcript I now want to solve some inequalities that also have absolute values in them. |

Solving an Absolute Value Equation with Two Unknown Variables |
The student does not understand how to write and solve absolute value inequalities. |

Set Up Two Equations |
Graphing absolute value equations and inequalities is a more complex procedure than graphing regular equations because you have to simultaneously show the positive and negative solutions. |

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If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.

Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.

Plug these values into both equations. Equation 2 is the correct one.

You can now drop the absolute value brackets from the original equation and write instead:Solving Absolute Value Equations and Inequalities 51 An absolute value inequality such as | x º 2|. What Are Some Words We Use To Write Inequalities?

Knowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge.

Arm yourself by learning some of the common phrases used to describe a compound inequality and an absolute value inequality. Absolute value equations and inequalities add a twist to algebraic solutions, allowing the solution to be either the positive or negative value of a number.

Graphing absolute value equations and inequalities is a more complex procedure than graphing regular equations because you have to simultaneously show the positive and negative solutions.

Solving Absolute Value Equations and Inequalities 51 An absolute value inequality such as |x º 2|.

The other case for absolute value inequalities is the "greater than" case. Let's first return to the number line, and consider the inequality | x | > 2.

The solution will be . Likewise, given an absolute value inequality such as |x – 5| 9, emphasize interpreting the solution set as all values within 5 units of nine.

Be sure to include situations that give rise to absolute value equations of the form | x – a | > b.

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Absolute Value Inequalities