An industrial laser cuts steel plates that are 11.93 meters long. the laser can have an error value of at most 0.02 meters. the inequality |x − | ≤ can be used to find the range of acceptable lengths for the steel plates. the range of acceptable lengths for the steel plates is ≤ x ≤

Step-by-step explanation:

Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...

  |x -11.93| ≤ 0.02

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We can solve this by "unfolding" it, then adding 11.93:

  -0.02 ≤ x -11.93 ≤ 0.02

  11.91 ≤ x ≤ 11.95

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.