Question

Use the drawing tool(s) to form the correct answer on the provided number line.

Eric wants to make sure he keeps an average speed of 70 miles/hour while testing his car’s engine. He allows the car’s speed to vary a certain number of miles/hour which can be modeled by the inequality |x − 70| ≤ 4. Plot the range of speeds Eric would not drive at under the given conditions.

Answer 1

Explanation:

In general, solutions to absolute value inequalities, as in this case, take two forms:

If | x | <a, then x<a or x> -a.

If | x |> a, then x> a or x <-a.

In this case, you have |x − 70| ≤ 4. So, you have two cases:

x − 70 ≤ 4 and x − 70 ≥ -4

Solving both equations:

x − 70 ≤ 4

x ≤ 4 + 70

x≤ 74

and

x - 70 ≥ -4

x ≥ -4+70

x ≥ 66

It is convenient to graph both solutions, as shown in the attached image .

The intersection between both conditions is the solution to the inequality (that is, in the image it is shown as the interval painted by both colors). In this case, the solution is 66≤x≤74

This indicates that Eric can drive within this speed range.

The range of speeds Eric would not drive at under the given conditions is x≤66 and x≥74, as shown in the other image.

Answer 2

see below

Explanation:

Eric will drive between 70 -4 = 66 mph and 70+4 = 74 mph. He will not drive less than 66 or more than 74 mph.