Question

Here is a table of the average distance and the variation in the distance for the five innermost planets in our solar system: Average Distance and Variation Planet Name Average Distance Variation Mercury 36.0 million miles 7.39 million miles Venus 67.2 million miles 0.43 million miles Earth 93.0 million miles 1.55 million miles Mars 142 million miles 13.2 million miles Jupiter 484 million miles 23.2 million miles "Average distance" means the mean distance that planet is from the sun over the course of its orbit, and "variation" means how far it varies from that mean. For example, if a planet had an average distance of 5 miles and a variation of one mile, it would have distances between 4 and 6 miles at different times. a) Write and solve an inequality to represent the range of distances that can occur between the Sun and one of the planets from the table (your choice). Show your steps/process. b) Why is this best represented as an inequality rather than an equation? Explain in at least 3 sentences.

Answer 1

9514 1404 393

Answer:

a) |e-93|≤1.55; 91.45 ≤ e ≤ 94.55

b) see below

Explanation:

a) Let e represent the distance from the sun to the earth in millions of miles. The table tells us the average distance is 93.0 million miles, and the difference from that value can be as much as 1.55 million miles. The corresponding inequality is ...

|e-93.0| ≤ 1.55

We can solve this by rewriting it as a compound inequality.

-1.55 ≤ e -93.0 ≤ 1.55

91.45 ≤ e ≤ 94.55 . . . . . . add 93

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b) An absolute value equation will give a finite number of particular values as its solution. The question asks for a range of values. An absolute value inequality is well-suited to providing a solution that is a range of values.