Complete the sentence. From the definition of absolute value,

3|x| =
when x > 0
and
3|x| =
when x < 0.

3|x| = 3x when x 0 and 3|x| = -3x when x < 0

Step-by-step explanation: Absolute value basically refers to the distance of a point from the origin (zero), regardless of the direction. The absolute value of a number is represented by two vertical lines enclosing the number. For example, |6| = 6, or in this case, 3|x| = 3x. Here, the value is replaced by the term "x". "x" is used as a term for an unknown value/variable. so basically, we're solving for x kinda. Multiplying "x" (the unknown variable) by 3 gives us = 3x. We know from the sign that x can't be below zero, only above or equal to. So, 3lxl = 3x when x is above or equal to the origin (zero). We know from the second problem that x can't be above zero because of the sign <, only below zero. Because we can only go below zero, that positive 3 turns negative. Multiplying x by -3 gives us = -3x. So, 3|x| = -3x when x is blow the origin (zero).

Note: the absolute value of a number is always positive, but in this scenario this rule doesn't apply because "x" is not a number, only a unknown value.

Sorry in advance if my explanation still doesn't make sense. Math isn't my thing really.

step-by-step explanation:

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