Maths-
General
Easy

Question

A company manufactures cell phone cases. the length of a certain case must be with in  of  as shown. All cases with lengths outside of this range are removed from the inventory How could you use an absolute value inequality to represent the lengths of all the cases that should be removed ? Explain.

hintHint:

|x| is known as the absolute value of x. It is the non-negative value of x irrespective of its sign. The value of absolute value of x is given by
vertical line x vertical line equals open curly brackets table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell negative x comma x less than 0 end cell row cell x comma x greater or equal than 0 end cell end table close space
We will construct an equation which models the situation with the help of the concept of absolute value.

The correct answer is: Thus, the equation representing the given situation is 𝑥 − 125 > 0.25



    Step by step solution:
    Given,
    Let the length of the case that should be removed be x
    Length of the case = 125 mm
    Error that is allowed in making the case = 0.25 mm
    We form an equation in terms of length of the case.
    The length of the case which is removed is either smaller than (125-0.25) mm or greater than (125+0.25)mm in length
    We can write the above lengths as

    x less than 125 minus 0.25
    And

     x greater than 125 plus 0.25
    We can rewrite the above equations as

    x minus 125 less than negative 0.25
    not stretchy rightwards double arrow negative left parenthesis x minus 125 right parenthesis greater than 0.25
    And

    X -125 > 0.25
    We combine the above two cases to get the following equation.
    Thus, the equation representing the given situation is

     vertical line x minus 125 vertical line greater than 0.25

    Absolute value of a variable has many uses in mathematics. Geometrically, the absolute value of a number may be considered as its distance from zero regardless of its direction. The symbol |.| is pronounced as ‘modulus’. We read |x| as ‘modulus of x’ or ‘mod x’

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