To solve this absolute value inequality, we will consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 4x-3 > 7
Adding 3 to both sides of the inequality, we get:
4x > 10
Dividing both sides by 4, we obtain:
x > 10/4
Simplifying the fraction, we get:
x > 5/2
Case 2: -(4x-3) > 7
Distributing the negative sign, we have:
-4x + 3 > 7
Subtracting 3 from both sides of the inequality, we get:
-4x > 4
Dividing both sides by -4 and reversing the inequality sign:
x < -1
Combining both cases, we find the solution to the inequality:
x < -1 OR x > 5/2
|4x-3|>7
x< blank or x> blank
type as integers or simplified fractions
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