a Plot the minimum and maximum values on a number line.
B
b Start with determining the midpoint by using the number line that we formed in Part A.
A
aNumber Line:
B
bAbsolute Value Equation:∣x−92950000∣=1550000
Practice makes perfect
a We are told that the minimum distance from Earth to the Sun is 91.4 million miles and that the maximum distance equals 94.5 million miles. We can plot the maximum and minimum distances on the number line.
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∣=Distancefrommidpoint
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=2Min+Max
Let's substitute the values for the maximum and minimum distances into the formula and simplify.
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.
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