1 The surface area S of a cube with edge length x is given b

1). The surface area S of a cube with edge length x is given by S(x) = 6x² for x > 0. Suppose the cubes your company manufactures are supposed to have a surface area of exactly 42 square centimeters, but the machines you own are old and cannot always make a cube with the precise surface area desired. Write an inequality using absolute value that says the surface area of a given cube is no more than 3 square centimeters away (high or low) from the target of 42 square centimeters.

2). Solve the inequality and express your answer in interval form.

Solution

S(x) = 6x² ; actual value should be 42 cm²

upper limit is 42 + 3, lower limit is 42 -3

Inequality is |S(x) - 42| <= 3

==> -3 <= S(x) - 42 <= 3

==> -3 +42 <= S(x) - 42 +42 <= 3 +42

==> 39 <= S(x) <= 45

==> 39 <= 6x² <= 45

==> 39/6 <= 6x²/6 <= 45/6

==> 13/2 <= x² <= 15/2

==> (13/2) <= x <= (15/2)

==> 2.5495 <= x <= 2.7386

Hence x belongs to [(13/2) , (15/2)] = [2.5495 , 2.7386]