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Here are some tips for Absolute Value Equations, which aligns with Florida state standards:

**Absolute Value Equation**

You must understand absolute values and inequalities to master this topic.

To review absolute value, see Absolute Value 1 and Absolute Value 2.

To review the Single Variable Inequalities topic, see here.

Where is the expression between the absolute value signs and A is a positive number,b | |

• when solving an equation with the form | A| = , solveb | |

or A = bA = - b | |

• when solving an equality with the form | A| < , solveb | |

- b < A < b | |

This rule is also true for ≤. | |

• when solving an equality with the form | A| > , solveb | |

or A < - bA > b | |

This rule is also true for ≥. |

**Example 1:** Equations

Solve for x.1. |

x| = 5Following the rules above, we get2. |x= 5 orx= -5.Answer:

x| = -1By definition of absolute value, |3. |x| is always positive. So there is noxvalue that will work in this equation.Answer:

x- 6| = 4

x - 6 = 4 or x - 6 = -4 x - 6 + 6 = 4 + 6 x - 6 + 6 = -4 + 6 x = 10 x = 2 Answer:

**Example 2:** Inequalities

Solve for x.1. |

x| ≥ 5Following the rules above, we get2. |7 -x≥ 5 orx≤ -5.Answer:

x| ≤ 2

-2 ≤ 7 - x ≤ 2 -2 ≤ 7 - x and 7 - x ≤ 2 -2 - 7 ≤ 7 - x - 7 7 - x - 7 ≤ 2 - 7 -9 ≤ -x -x ≤ -5 9 ≥ x x ≥ 5 Combine the results: 9 ≥ x≥ 5

This is the same as 5 ≤x≤ 9

Answer:3. |8 -

x| > 2

8 - x < -2 or 8 - x > 2 8 - x - 8 < -2 - 8 8 - x - 8 > 2 - 8 -x < -10 -x > - 6 x > 10 x < 6 Answer:

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