Absolute value equation Absolute value equation : 4*|8x - 8| < 32
3 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
We have to solve 4*|8x - 8| < 32
4*|8x - 8| < 32
=> |8x - 8| < 8
=> |x - 1| < 1
-1 < (x - 1) < 1
-1 < (x - 1)
=> 0 < x
(x - 1) < 1
=> x < 2
The values of x lie in the interval (0, 2)
Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian
4*|8x - 8| < 32
Isolate the absolute value
| 8x - 8 | < 8
Divide out the eights
| x - 1 | < 1
x - 1 < 1 and x - 1 > -1
x < 2 and x > 0
so 0 < x < 2 is your interval.
giorgiana1976 | College Teacher | (Level 3) Valedictorian
We'll simplify the given expression, dividing it by 4 both sides:
4*|8x-8|<32
|8x-8|<8
Now, we'll discuss the absolute value of the expression 8x-8:
Case 1) 8x-8 for 8x-8>=0
8x>=8
x>=1
We'll solve the inequality:
8x-8 < 8
8x < 16
We'll divide by 8:
x < 16/8
x < 2
The interval of admissisble value of x, in this case, is [1, 2).
Case 2) -8x+8, for 8x-8<0
8x<8
x<1
We'll solve the inequality:
-8x+8 < 8 <=> -8x< 0
8x > 0
x > 0
The interval of possible values for x, in this case, is (0 , 1).