Which set notation correctly expresses the solution set to the equation 31−9x=4?(1 point)
Responses
(3)
{3}
(x=3)
{x=3}
{x=3}
The correct set notation that expresses the solution set to the equation 31-9x=4 is {x=3}.
The correct set notation that expresses the solution set to the equation 31−9x=4 is {x=3}.
To understand why this is the correct notation, let's break down the equation and solve for x.
Given equation: 31−9x=4
To solve for x, we need to isolate the variable. We can start by subtracting 31 from both sides of the equation:
31−31−9x = 4−31
-9x = -27
Next, we divide both sides of the equation by -9 to solve for x:
(-9x)/(-9) = (-27)/(-9)
x = 3
Therefore, the solution to the equation is x = 3.
Now, let's understand the set notation used to express the solution set. In set notation, braces { } are used to indicate a set, and the variable x is written with an equality sign (=) to indicate its value. Thus, the set notation {x=3} conveys that the solution set consists of the single element x, where x is equal to 3.
Therefore, the correct set notation that expresses the solution set to the equation 31−9x=4 is {x=3}.