We are given the inequality:

$\left\vert\frac{4\text{ }-\text{ }7}{4}\right\vert \leq \frac{1}{3}$

Let's break this down step by step.

1. First, calculate the expression inside the absolute value:

$4 - 7 = -3$

Thus, the expression becomes:

$\left\vert\frac{-3}{4}\right\vert$

2. Next, simplify the fraction:

$\frac{-3}{4} = -0.75$

3. The absolute value of $-0.75$ is:

$\left\vert -0.75 \right\vert = 0.75$

4. Now, we compare $0.75$ to $\frac{1}{3}$:

$0.75 \leq \frac{1}{3}$

Since $\frac{1}{3} \approx 0.3333$, the inequality $0.75 \leq 0.3333$ is false.

Conclusion:

The inequality is not true.

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Would you like more details or have any questions? Here are 5 related questions:

1. What happens when the absolute value symbol is removed in inequalities?
2. Can you solve inequalities involving more complex absolute value functions?
3. How does this inequality change if the right side were $\frac{3}{4}$?
4. What is the general approach to solving inequalities with fractions?
5. How do absolute values affect equations compared to inequalities?

Tip: When solving inequalities with absolute values, always check both the positive and negative scenarios to ensure you don't miss any potential solutions!