Equation is |x − 20| = 0.45
The min is x = 19.55
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Explanation:
fl oz = fluid ounces
x = volume of the drink in fl oz
The expression |x-20| represents how far x is from the target of 20 fl oz. We use absolute value to ensure the result is never negative. It might help to draw out a number line.
Two examples:
- If x = 22 then |x-20| = |22-20| = |2| = 2 which shows that 22 is 2 units away from 20 on the number line.
- If x = 17 then |x-20| = |17-20| = |-3| = 3 which shows that 17 is 3 units away from 20 on the number line.
We want this difference to be within 0.45 fl oz, i.e. we want |x-20| to either equal 0.45 or be smaller than it.
If we only cared about the min and max, then we set |x-20| equal to 0.45 to generate the equation |x − 20| = 0.45
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Solve this equation to find the min and max.
|x - 20| = 0.45
x-20 = 0.45 or x-20 = -0.45
x = 0.45+20 or x = -0.45+20
x = 20.45 or x = 19.55
The min is 19.55 fl oz and the max is 20.45 fl oz.
Phrased another way: the x values span from 19.55 to 20.45, inclusive of both endpoints. We could write as a compact way to describe what values x could be.