|8x-2|-6=2

Answer 1

We need to solve the equation |8x-2|-6=2.

First, we can isolate |8x-2| by adding 6 to both sides of the equation:
|8x-2| = 2+6
|8x-2| = 8

Then, we can split the equation into two cases, one for when 8x-2 is positive and one for when it is negative.

Case 1: 8x-2 is positive:
8x-2 = 8
Adding 2 to both sides:
8x = 8+2
8x = 10
Dividing both sides by 8:
x = 10/8
Simplifying the fraction:
x = 5/4

Case 2: 8x-2 is negative:
-(8x-2) = 8
Multiplying both sides by -1 to switch the sign:
8x-2 = -8
Adding 2 to both sides:
8x = -8+2
8x = -6
Dividing both sides by 8:
x = -6/8
Simplifying the fraction:
x = -3/4

Therefore, the solutions to the equation |8x-2|-6=2 are x = 5/4 and x = -3/4.

Answer 2

|3-2x|<5

Answer 3

We need to solve the inequality |3-2x| < 5.

First, we can isolate |3-2x| by setting up two different inequalities, one for when 3-2x is positive and one for when it is negative.

Case 1: 3-2x is positive:
3-2x < 5
Subtracting 3 from both sides:
-2x < 5-3
-2x < 2
Dividing both sides by -2 and reversing the inequality:
x > 2/-2
x > -1

Case 2: 3-2x is negative:
-(3-2x) < 5
Multiplying both sides by -1 to switch the inequality sign:
2x-3 < 5
Adding 3 to both sides:
2x < 5+3
2x < 8
Dividing both sides by 2:
x < 8/2
x < 4

Therefore, the solutions to the inequality |3-2x| < 5 are x > -1 and x < 4.

Answer 4

|3-2x|≤5

Answer 5

We need to solve the inequality |3-2x| ≤ 5.

First, we can isolate |3-2x| by setting up two different inequalities, one for when 3-2x is positive or zero and one for when it is negative.

Case 1: 3-2x is positive or zero:
3-2x ≤ 5
Subtracting 3 from both sides:
-2x ≤ 5-3
-2x ≤ 2
Dividing both sides by -2 and reversing the inequality:
x ≥ 2/-2
x ≥ -1

Case 2: 3-2x is negative:
-(3-2x) ≤ 5
Multiplying both sides by -1 to switch the inequality sign:
2x-3 ≤ 5
Adding 3 to both sides:
2x ≤ 5+3
2x ≤ 8
Dividing both sides by 2:
x ≤ 8/2
x ≤ 4

Therefore, the solutions to the inequality |3-2x| ≤ 5 are x ≥ -1 and x ≤ 4.