Question

Solve the equation below, and check the solution. 0.3x = 9 The solution set is { }

Answer 1

Answer:

  {30}

Step-by-step explanation:

The solution set can be written a couple of ways:

Roster: lists the elements of the set:

  x = {30}

Set builder notation: defines the elements of the set according to some rule or rules

  {x : x = 30}

The latter form can have variations that define the domain of x on the left, such as

  $\{x\in\mathbb{Z}:x=30\}$

This is pronounced, "x is an element of the set of integers such that x is equal to 30." This sort of notation is more commonly used when the set is specified by an inequality or a functional relationship. You may see the colon (:) replaced by a vertical bar (|).

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Comment on the above notations

I don't like the notation x = {30} because the solution to the equation is a value, not a set of values. I prefer to write it as x ∈ {30}. "x is an element of the set containing 30." The "is an element of" symbol (∈) is not always available, so the equal sign is often used instead.