Absolute value of 4x minus 3 greater than minus 4 

To solve the inequality involving the absolute value, we start with:

\[
|4x - 3| > -4
\]

Since the absolute value of any expression is always non-negative (i.e., greater than or equal to zero), it will always be greater than \(-4\) because \(-4\) is a negative number. 

Therefore, the inequality holds for all real values of \( x \).

**Conclusion:**
\[
\text{The solution is } x \in \mathbb{R} \text{ (all real numbers)}.
\]

Would you like further details or have any questions?

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Here are some related questions you might find helpful:
1. What is the difference between absolute inequalities and regular inequalities?
2. How do we solve inequalities where absolute value is less than a negative number?
3. What if the inequality were \( |4x - 3| \geq 4 \) instead?
4. How do absolute values change when applied to inequalities?
5. Can we represent the solution of \( |4x - 3| > -4 \) on a number line?

**Tip:** When solving inequalities with absolute values, always check if the inequality involves a negative on the other side—absolute values are always non-negative, so the inequality might simplify instantly.

Absolute value of 4x minus 3 greater than minus 4

Discover the solution to the absolute value inequality |4x - 3| > -4. This problem explores the properties of absolute values in inequalities, explaining why the inequality holds true for all real numbers. Ideal for students in Grades 9-10.

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