Absolute Value Equations

Rules/Problems

100

The first step when solving an absolute value equations

What is, solve for the absolute value

200

The second step of solving an absolute value equation (after solving for the absolute value)

What is, we must split the equation into 2 equations (positive, negative)

300

The definition of absolute value

What is, the distance a value is from zero

400

The answer is no solution 

What is, when an absolute value is set equal to a negative

500

Is there a way to have only one solution (other than no solution)? 

If so give an example!

What is, when an absolute value is set equal to zero

Problems (1)

100

| z | = 4

What is, { -4 , 4 }

200

| d + 1 | = 7

What is { 6 , -8 }

300

5 | q + 6 | = 20

What is { -2 , -10 }

400

| p + 1 | + 10 = 5

What is { No Solution }

500

2 | 3x - 4 | + 8 = 6

What is No Solution

Problems (2)

100

| d  | = 9

What is { 9 , -9 }

200

| a - 6 | = 10

What is { 16 , -4 }

300

3 | r - 4 | = -21

What is No Solution

400

6 | g - 3 | = 42

What is { 10 , -4 }

500

4 | 7y + 2 | - 8 = -7

What is { -.25 , -.32 }

Problems (3)

100

| w + 9 | = 17

What is { 8 , -26 }

200

2 | x + 5 | = 22

What is { 16 , -6 }

300

3 | 2a - 4 | = 0

What is { 2 }

400

2 | y + 4 | = 14

What is { 3 , -11 }

500

-3 | 3t - 2 | -12 = -6

What is { No Solution }

Problems (4)

100

| x - 6 | = 35

What is { 41 , -29 }

200

| t + 9 | - 8 = 5

What is { 4 , -22 }

300

8 | 5w - 1 | = 0

What is { 1/5 }

400

| 3b - 10 | = 2b

What is { 10 , 2 }

500

-5 | 3z + 8 | - 5 = -20

What is {-5\3 & -11/3 }