Answer:
Step-by-step 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.
