# Absolute value equation Absolute value equation : 4*|8x - 8| < 32

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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)**

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.

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).**