At a trout farm, most of the trout have a length of 23.5 cm. The length of some differ from this by as much as 2.1 cm. Write and solve an absolute-value inequality to find the range of lengths of the trout.

21.4 ≤ x ≤ 25.6

Step-by-step explanation:

The absolute value of a number is the non-negative value of the number without regard to its sign.

The absolute value of a real number x (|x|) is x for x is positive and -x for x is negative.

Let x represent the length of the trout. Since most trout have a length of 23.5 cm and differ by 2.1 cm, then x can be represented by:

|x - 23.5| ≤ 2.1

x - 23.5 ≤ 2.1 or -(x - 23.5) ≤ 2.1

x ≤ 2.1 + 23.5 or x - 23.5 ≥ -2.1

x ≤ 25.6 or x ≥ 21.4

Hence, the range of lengths of the trout is 21.4 ≤ x ≤ 25.6

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step-by-step explanation:

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(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0