Final Answer:
The ordered values from least to greatest are: \(-|-\frac{3}{2}|\), \(-7\), \(-|4|\), \(0\), \(\frac{1}{4}\), \(0.6\), \(|6|\), \(5\).
Step-by-step explanation:
To order the given values from least to greatest, let's first consider the absolute values. The smallest absolute value is \(-|\frac{3}{2}|\), followed by \(-7\), and then \(-|4|\). The negative values are placed first in the order. Next, we have \(0\) and \(\frac{1}{4}\), with \(0\) coming before \(\frac{1}{4}\). Finally, the positive values are ordered with \(0.6\) preceding \(|6|\), and \(5\) is the largest value.
Starting with the absolute values helps in determining the order of the negative and positive values separately. The negative values are ordered based on their absolute magnitudes, followed by the non-negative values in ascending order. This step-by-step approach ensures a systematic arrangement of the given values.
In summary, the ordered sequence from least to greatest is obtained by first considering the absolute values and then arranging the negative and non-negative values accordingly. This process provides a clear and organized way of comparing and ordering the given numerical expressions.