Create and solve a one-variable linear equation from a short context.
Solve an absolute-value equation as distance from a target
Problem
A temperature is exactly \(6^{\circ}\text{F}\) from a target of \(72^{\circ}\text{F}\). Let \(T\) represent the temperature in degrees Fahrenheit. Use an absolute-value equation to determine all possible values of \(T\).
Big Picture
What this problem is really about
Absolute value is useful here because it measures distance from a target. We’ll express the temperature’s distance from the target as an absolute-value equation, then split that equation into the position above the target and the position below it. Solving both cases finds every temperature at the required distance.
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