What is the value of this expression when $g=-3.5$?
$8-|2 g-5|$
We are given the algebraic expression \(8 - |2g - 5|\) and asked to evaluate it when \(g = -3.5\). The absolute value function \(|x|\) returns the distance of \(x\) from zero on the number line, which is always non-negative. Specifically, \(|x| = x\) if \(x \geq 0\) and \(|x| = -x\) if \(x < 0\). We need to substitute the given value of \(g\) into the expression and follow the order of operations to find the result.
Substitute \(g = -3.5\) into the term inside the absolute value bars, which is \(2g - 5\):
\[2(-3.5) - 5 = -7 - 5 = -12.\]
Now, we apply the absolute value to this result:
\[|-12| = 12.\]
The expression then becomes:
\[8 - 12 = -4.\]
Following the calculation, we found the value of the expression is \(-4\). Comparing this result to the given options (\(20, 10, 6, -4\)), the correct choice is \(-4\). Therefore, the value of the expression \(8 - |2g - 5|\) when \(g = -3.5\) is \(-4\).
Understanding how to evaluate expressions with absolute values is essential for calculating distances, differences, or magnitudes in real-world scenarios. For example, if you are measuring temperature variations relative to a baseline, the absolute value can represent the magnitude of the deviation, regardless of whether the temperature is above or below that baseline. If the baseline is \(5^\circ\) and the temperature is \(2g\), where \(g\) is a scaling factor, \(|2g - 5|\) helps determine the total deviation from the baseline. This skill is useful in fields like engineering, finance, and physics to ensure calculations remain consistent and accurately reflect magnitude.