Create and solve one-variable equations and inequalities, including absolute-value, linear, quadratic, simple rational, and exponential cases.
Create and solve an absolute-value inequality from a distance-from-target statement
Problem
A manufactured part is acceptable when its length is \(\text{no}~\text{more}~\text{than}~0.2~\text{cm}\) from a target length of \(10~\text{cm}\). Let \(x\) be its length in centimeters. Use the displayed number line to write and solve an absolute-value inequality for \(x\).
Two unknown boundary lengths are each 0.2 centimeter from target 10 centimeters.Open full size
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What this problem is really about
The tolerance describes all lengths whose distance from the target is no greater than the allowed amount. We’ll express that distance with absolute value, convert the inclusive tolerance into a compound inequality between a lower and upper deviation, and then shift both bounds back to actual lengths.
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