A plant that manufactures metal plates has a quality control team to check that the plates are the right size.

Question

A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate with dimensions 5 cm by 3 cm must have length within 0.25 cm of 5 cm. Write and solve an absolute value inequality to find the minimum and maximum area of the plates. (Round to the nearest hundredth)

Minimum ___ cm^2

Maximum___ cm^2

Answer 1

So we know 5-.25 ≤ L ≤ 5+.25

4.75 ≤ L ≤ 5.25

The area of a rectangle is Length*Width. Here Width = 3. So area is 3*L

3*(4.75) ≤ 3*L ≤3*(5.25)

14.25 ≤ 3*L ≤ 15.75

Minimum area is 14.25 cm²

Maximum area is 15.75 cm²

Answer 2

|x - 5| < 0.5

assuming x - 5 ≥ 0

x - 5 < 0.5

x < 5.5

assuming x - 5 < 0

-(x - 5) < 0.5

-x + 5 < 0.5

-x < -4.5

x > 4.5