b We are given the minimum and maximum lengths and asked to write an absolute value equation to represent these lengths. First, let's write an equation for the distance of a point

x

from the midpoint.

∣ x - Midpoint ∣ = Distance from midpoint

To write an equation that models the situation, we can think of the given

minimum

and

maximum

distances as solutions to the equation. Considering the number line that we formed, we can find the midpoint using the following formula.

Mid = \frac{Min + Max}{2}

Let's substitute the values for the maximum and minimum distances into the formula and simplify.

Mid = \frac{Min + Max}{2}

SubstituteII

$Min = 91.4$ , $Max = 94.5$

Mid = \frac{9 1 . 4 + 9 4 . 5}{2}

AddTerms

Add terms

Mid = \frac{1 8 5 . 9}{2}

CalcQuot

Calculate quotient

Mid = 92.95

We found that the midpoint is

92.95

million miles. Since this is a midpoint, it means that the distances from the minimum and maximum value to the midpoint are the same.

max - mid = mid - min

Therefore, it will be enough to evaluate either side of the equality. Let's evaluate the left-hand side.

Max - Mid

SubstituteII

$Max = 94.5$ , $Mid = 92.95$

94.5 - 92.95

SubTerm

Subtract term

1.55

The distance is

1.55

million miles. Let's illustrate this on the number line.

As a result, we can substitute the found values into the absolute value equation. Keep in mind that all the values we found are expressed in millions.

∣ x - 92950000 ∣ = 1550000

Exercise