a.

A certain template is long.

Observe the table:

Write an absolute value inequality for templates with each line color.

Let represents the length for the part of a car.

Red:

Rewrite the inequality is .

Blue:

Rewrite the inequality is .

Green:

Rewrite the inequality is .

b.

Find the acceptable lengths for that part of a car if the template has each line color.

The acceptable length for the part of the car if the template has red line color:

                                                     (The inequality)

(Add to each side)

                             (Apply additive inverse property: )

                                                    (Simplify)

The acceptable length for the part of the car if the template has blue line color:

                                                     (The inequality)

(Add to each side)

                             (Apply additive inverse property: )

                                                    (Simplify)

The acceptable length for the part of the car if the template has green line color:

                                                           (The inequality)

     (Add to each side)

                                 (Apply additive inverse property: )

                                                    (Simplify)

c.

Graph the solution set for each line color on a number lines are

Red: .

Blue: .

Green: .

d.

Observe the graph,

Find the tolerance of which line color includes the tolerances of the other line colors.

Red;The red line color has the smallest tolerance, .

So, the other line colors would be well within their tolerances.

a.

Red: .

Blue: .

Green: .

b.

Red: .

Blue: .

Green: .

c.

Graph the solution sets are , and .

d.

Red color line includes the tolerances of the other line colors.