Step: 1

As, | 4x + 9 | = 8, then the values of the expression 4x + 9 is equal to 8 or - 8.

Step: 2

4x + 9 = 8 or 4x + 9 = - 8

Step: 3

4x + 9 - 9 = 8 - 9 or 4x + 9 - 9 = - 8 - 9

[Subtract 9 from each side.]

Step: 4

4x = -1 or 4x = - 17

[Simplify.]

Step: 5

[Divide by 4 on each side.]

Step: 6

The solutions of the equation are - 1 4 and - 17 4 .

Correct Answer is : - 1 4 , - 17 4

Step: 1

| x - 8 | - 5 = - 0.35

[Original equation.]

Step: 2

| x - 8 | - 5 + 5 = - 0.35 + 5

[Add 5 on both sides.]

Step: 3

| x - 8 | = 4.65

[Simplify.]

Step: 4

| x - 8 | = 4.65, then x - 8 equals 4.65 or - 4.65

Step: 5

Step: 6

[Add 8 on both sides.]

Step: 7

[Simplify.]

Step: 8

The solutions of the equation are 12.65 and 3.35.

Correct Answer is : 12.65, 3.35

Step: 1

| 5x | = 2.85

[Original equation.]

Step: 2

As, | 5x | = 2.85 then the values of the expressions 5x equals to 2.85 or - 2.85

Step: 3

5x = 2.85 or 5x = - 2.85

Step: 4

[Divide by 5 on both sides.]

Step: 5

The solutions of the equation are 0.57 and - 0.57.

Correct Answer is : 0.57, - 0.57

Step: 1

| x - 2 | = 10

[Original Equation.]

Step: 2

Step: 3

[Add 2 to each side.]

Step: 4

[Simplify.]

Step: 5

The solutions of the equation are 12 and - 8.

Correct Answer is : 12, - 8

Step: 1

|x - 3| = 7

Step: 2

[Write it as disjunction.]

Step: 3

Step: 4

Check the answer: x = 10

Step: 5

|10 - 3| = 7

Step: 6

7 = 7, which is true.

Step: 7

So, x = 10 is the solution.

Step: 8

Check the answer: x = - 4

Step: 9

|- 4 - 3| = 7

Step: 10

|- 7| = 7

Step: 11

7 = 7, which is true.

Step: 12

So, x = - 4 is the solution.

Step: 13

The graph for the solution:

Correct Answer is : Graph 2

Step: 1

|x + 7| = 9

Step: 2

[Write it as disjunction.]

Step: 3

Step: 4

Check the answer: x = 2

Step: 5

|2 + 7| = 9

Step: 6

9 = 9, which is true.

Step: 7

So, x = 2 is the solution.

Step: 8

Check the answer: x = - 16

Step: 9

|- 16 + 7| = 9

Step: 10

|- 9| = 9

Step: 11

9 = 9, which is true.

Step: 12

So, x = - 16 is the solution.

Step: 13

The graph for the solution is:

Correct Answer is : Graph 2

Step: 1

|x | - 2 = 5

Step: 2

|x | = 7

[Add 2 to both sides of the equation.]

Step: 3

[Write it as disjunction.]

Step: 4

Check the answer: x = 7

Step: 5

|7| - 2 = 5

Step: 6

5 = 5, which is true.

Step: 7

Hence, x = 7 is the solution.

Step: 8

Check the answer: x = - 7

Step: 9

|- 7| - 2 = 5

Step: 10

5 = 5, which is true.

Step: 11

So, x = - 7 is also the solution.

Step: 12

The graph for the solution is:

Correct Answer is : Graph 4

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