Find, in the set of real numbers,
the solution set of the equation 𝑥 minus three root three is equal to root
In this question, we are given an
equation in a variable 𝑥 and asked to find the solution set of the equation over
the set of real numbers. To do this, we can start by
recalling that the solution set of an equation over a set is the set of all values
that satisfy the equation in that set. So, in this case, we want to find
the set of all real values of 𝑥 that satisfy the given equation.
In an equation, both sides of the
equation must be the same. This means that we can apply the
same operations to both sides of the equation to leave them equal. We can use this to solve for 𝑥 by
isolating 𝑥 on one side of the equation. To isolate 𝑥 on the left-hand side
of the equation, we need to remove the constant value of negative three root
three. We can do this by adding three root
three. We need to add this value to both
sides of the equation to make sure that they are still equal.
On the left-hand side of the
equation, we have negative three root three plus three root three is zero, so we are
left with 𝑥. On the right-hand side, we have
root three plus three root three. We can simplify the right-hand side
of the equation by noting that both terms share a factor of root three. Taking this factor out yields one
plus three all multiplied by root three, which is equal to four root three.
We have shown that the only
solution to the equation is 𝑥 equals four root three. However, remember that we are asked
to find the solution set of the equation over the real numbers. This means that we need to check
all of the solutions are real numbers and give our answer as a set. Of course, we know that four root
three is a real number. And so we have shown that the
solution set of the given equation over the set of real numbers is the set
containing only the value of four root three.