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 cars engine. he allows the cars 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 drives at under the given conditions.
(image of drawing tools and number line with speed (miles/hour) from 60 to 80)

Explanation:

Step1: Solve the absolute value inequality

The inequality is \(|x - 70| \leq 4\). By the definition of absolute value, this means \(-4 \leq x - 70 \leq 4\).

Step2: Solve for x

Add 70 to all parts of the compound inequality: \(70 - 4 \leq x \leq 70 + 4\), which simplifies to \(66 \leq x \leq 74\). This is the range of speeds Eric does drive at. So the speeds he does not drive at are \(x < 66\) or \(x > 74\).

Step3: Plot the ranges

On the number line, for \(x < 66\), we draw a ray starting from an open point at 66 (since 66 is not included) going to the left. For \(x > 74\), we draw a ray starting from an open point at 74 (since 74 is not included) going to the right.

Answer:

To plot the speeds Eric would not drive at:

• Draw an open point at 66 and a ray extending to the left (for speeds less than 66).
• Draw an open point at 74 and a ray extending to the right (for speeds greater than 74).