Solve each absolute value equation and match them with the correct solution.

Step-by-step explanation:

First we must understand that absolute value of a function returns both positive and negative function.

1) Given |x-6| = 5

For the positive value of the function:

x-6 = 5

Add 6 to both sides

x-6+6 = 5+6

x = 11

For the negative function:

-(x-6) = 5

Open the parentheses

-x+6 = 5

Subtract 6 from both sides

-x+6-6 = 5-6

-x = -1

x = 1

Hence x = 1, x = 11

2 ) Given |3x-7| = 12

For the positive value of the function:

3x-7 = 12

Add 7 to both sides

3x-7+7 = 12+7

3x = 19

x = 19/3

For the negative function:

-(3x-7) = 12

Open the parentheses

-3x+7 = 12

Subtract 7 from both sides

-3x+7-7 = 12-7

-3x = 5

x = -5/3

Hence x = 19/3, x = -5/3

3) Given |2x+9| - 10= 5

For the positive value of the function:

2x+9-10= 5

2x-1 = 5

Add 1 to both sides

2x-1+1 = 5+1

2x = 6

x= 3

For the negative function:

-(2x+9)-10 = 5

Open the parentheses

-2x-9-10 = 5

-2x-19 = 5

Add 19 to both sides

-2x-19+19 = 5+19

-2x= 24

x = -24/2

x= -12

Hence x = 3, x = -12

4) ) Given |5x-3|+12 = 4

For the positive value of the function:

5x-3+12= 4

5x+9 = 4

Subtract 9 from both sides

5x+9-9 = 4-9

5x = -5

x= -1

For the negative function:

-(5x-3)+12= 4

Open the parentheses

-5x+3+12 =4

-5x+15 = 4

Subtract 15 from both sides

-5x+15-15 = 4-15

-5x = -11

x = 11/5

Hence x = -1, x = 11/5

because they could drop even lower..