Answer:
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