# Absolute Value Equations Worksheets

What Are Absolute Value Equations? An equation having the absolute value of the expression is called absolute value equations. It is represented by |x|=a. It is usually written in modulus form such as |x|=a. The equation of such type has two solutions which include x = a and x = -a. It represents that both the numbers are at a distance from 0. If you encounter a problem having absolute equations, then you can solve it by making two different equations and then address them individually. For example; |x+8|=16
|x+8|=16 The solution goes as follows; x+8=16. Now subtracting 8 from both sides x + 8 - 8 = 16 - 8. Therefore, x= 8 The other way of solving the absolute value equations is as such; x + 8 = -16. In order to remove the modulus sign, we must encounter the change of the sign (i.e., either positive or negative). Now subtracting 8 from both sides, we get x + 8 - 8 = -16 - 8, x= -24. However, this represents that the absolute value equation with a negative number has no solution. Have you ever heard of a distance that you travel in a negative way? That is why the solution to such an equation is not possible.

• ### Basic Lesson

Demonstrates how to estimate round to the nearest thousand. Also includes practice problems. When you are rounding you are converting a number into an easier number to work with. When rounding always ask yourself if the number is 5 or more you increase the number to the left by one and drop all numbers to the right to zero.

• ### Intermediate Lesson

Uses a larger more difficult numbers to round than the basic lesson. Round 156 to the nearest hundred. The number you are changing is the 1. The number directly to the right of one is 5. Since this number is 5 or more, the hundreds digit 1 increases to 2 and all numbers to the right are changed to zero. 156 rounded to the nearest hundred is 200.

• ### Independent Practice 1

20 problems ask you to round to the nearest thousand. The answers can be found below.

• ### Independent Practice 2

20 practice problems that review estimating round to the nearest thousand. The answers can be found below.

• ### Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

• ### Skill Quiz

10 problems that test rounding to the nearest thousand skills.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Answer Key

Answers for the lesson and practice sheets.

• ### Basic Lesson

Guides students solving equations that involve an Absolute Value Equations. Demonstrates answer checking.

• ### Intermediate Lesson

Demonstrates how to solve more difficult problems.

• ### Independent Practice 1

A really great activity for allowing students to understand the concept of Absolute Value Equations.

• ### Independent Practice 2

Students find the Absolute Value Equations in assorted problems. The answers can be found below.

• ### Homework Worksheet

Students are provided with problems to achieve the concepts of Absolute Value Equations.

• ### Skill Quiz

This tests the students ability to evaluate Absolute Value Equations.

• ### Homework and Quiz Answer Key

Answers for math worksheets, quiz, homework, and lessons.

#### H.L. Mencken

The best teacher is not the one who knows most, but the one who is most capable of reducing knowledge to that simple compound of the obvious and wonderful...