x b
Algebra 1P: Standard 3: Name __________________________
Solving Absolute Value Equations Homework Worksheet # 1
Things to know: I know…

The absolute value of a number means its distance from zero.

To find the distance between 2 numbers, x and b , I calculate the absolute value of their difference: the distance from x to b or from b to x = | x – b | = | b – x |.

If the | x – b | = c , then x is c units from b in either direction.
Draw graphs for the following equations:
1. | x | = 3 2. | x | = 2 3. | x – 0 | = 5
-6 -4 -2 0 2 4 6 x = _____ or x = ______
4. | x – 1 | = 3
-6 -4 -2 0 2 4 6 x = _____ or x = ______
5. | x – 4 | = 2
-6 -4 -2 0 2 4 6 x = _____ or x = ______
6. | x + 1 | = 5
-6 -4 -2 0 2 4 6 x = _____ or x = ______
7. | x + 2 | = 3 x = _____ or x = ______
10. | x – 4 | = 1
-6 x
-4 -2 0 2 4 6
= _____ or
8. | x – 5 | = 0 x = ______
-6 x
-4 -2 0 2 4 6
= _____ or
9. | x + 3 | = 4 x = ______ x = _____ or x = ______
11. | x + 4 | = 2 x = _____ or x
12. | x + 1 | = -5
= ______ x = _____ or x = ______ x = _____ or x = ______ x = _____ or x = ______
13. Graph the solutions for x if | x – b | = c . Which value is plotted first? _______ Which value tells the distance? __________ Label the solution points in terms of b and c .
What can x equal? x = ___________ or x = ____________

Algebra 1P: Standard 3: Name __________________________
Solving Absolute Value Equations Homework: Worksheet # 2
Things to know: I know…

The absolute value of a number means its distance from zero.

To find the distance between 2 numbers, x and b , I calculate the absolute value of their difference: the distance from x to b or from b to x = | x – b | = | b – x |.
EX:

If the | x – b | < 6, then x is less than 6 units from b in either direction.

If the | x – b | > 6 number, then x is greater than 6 units from b in either direction.
Draw graphs for the following inequalities; then write the algebraic solutions:
1. | x | > 2 2. | x | < 5 3. | x – 0 | > 4 x < _____ or x > ______
4. | x – 1 | < 3
_____ < x < ______
5. | x – 4 | > 2 x < _____ or x > ______
6. | x + 1 | < 4
_____ < x < ______
7. | x + 2 | > 3
____________________
10. | x – 4 | < -1 x < _____ or x > ______
8. | x – 5 | < 0
____________________
11. | x + 4 | > 2
_____ < x < ______
9. | x + 3 | > 0
____________________
12. | x + 1 | < 5
____________________ ____________________
13. Graph the solutions for x if | x – b | < c .
___________________
Which value ( b or c ) is plotted first? ____________Which value tells the distance? ___________
Are the possible x values in one continuous region or two separate pieces of the graph? ____________ x
14.
What can x equal? _______________________
Graph the solutions for x if | x – b | > c . Is the set of possible x values one continuous region or two separate pieces of the graph? ____________
What can x equal? _______________________ x

Algebra 1P: Standard 3: Name __________________________
Solving Absolute Value Equations Homework: Worksheet # 3
Example: | 5 – 2x | < 3
2 x
-6 -4 -2 0 2 5 8
Graph 2 x : all points 3 or less units away from 5; 5-3 = 2 and 5+3 =8
Solution for 2 x : All points between and including 2 and 8.
Graph x: divide the solution for 2 x by 2: 2/2 = 1 and 8/2 = 4. x
0 1 5/2 4
Solution for x : All points between 1 and 4, inclusive.
| 5 – 2x | < 3

5 – 3 < 2x < 5 + 3
2 < 2x < 8
1 < x < 4
Solve the following absolute value inequalities first for ax and then for x . Draw the graph and write the algebraic solution statement for each of the following problems:
1. | 3x | > 2 2. | 2x | < 5 3. | 4x – 0 | > 8
3 x 2 x 4 x x x
3 x < _____ or 3 x > ______ x < _____ or x > ______
4. | 2x – 1 | > 3
2x 5x
_____ < 2 x < ______
_____ < x < ______
5. | 5x – 4 | < 2 x
4 x < _____ or 4 x > _____ x < _____ or x > ______
6. | 4 – 3x | < 4
3x x
2 x < _____ or 2 x > ______ x < _____ or x > ______
7. | 6x + 2 | > 4
6x x
6 x : __________________ x : _________________ x x
5 x x
_____ < 5 x < ______
_____ < x < ______
8. | 7 – 5x | < 3
5 x : __________________ x : __________________
_____ < 3x < _____
_____ < x < _____
9. | 2x + 3 | > 5
2 x x
2 x : __________________ x : ___________________