Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Write and solve an absolute-value equation from a distance-from-a-target statement
Problem
A measurement is \(3~\text{units}\) from target \(20\). Let \(x\) represent the measurement. Use the displayed number line to write an absolute-value equation and solve for \(\text{both}~\text{possible}~\text{measurements}\).
Two unknown measurements are each 3 units from target 20.Open full size
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What this problem is really about
This is a distance-from-a-target situation, so absolute value captures how far the measurement is from the target without choosing a direction. We’ll set that distance equal to the given amount, split it into equal moves to the left and right, and solve both cases to recover the two possible measurements.
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