Sure, let's solve the problem step-by-step.
1. Define the unknown number:
Let [tex]\( x \)[/tex] be the unknown number we need to find.
2. Set up the equation:
According to the problem, five added to one third of this number is equal to twice the number. Mathematically, this can be written as:
[tex]\[
5 + \frac{1}{3}x = 2x
\][/tex]
3. Eliminate the fraction:
To remove the fraction, we can multiply every term in the equation by 3:
[tex]\[
3 \cdot 5 + 3 \cdot \frac{1}{3}x = 3 \cdot 2x
\][/tex]
4. Simplify the equation:
When we simplify, it becomes:
[tex]\[
15 + x = 6x
\][/tex]
5. Rearrange to isolate the variable [tex]\( x \)[/tex]:
We need to get all the terms involving [tex]\( x \)[/tex] on one side of the equation. So, we subtract [tex]\( x \)[/tex] from both sides:
[tex]\[
15 = 6x - x
\][/tex]
Simplify the right side:
[tex]\[
15 = 5x
\][/tex]
6. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], divide both sides of the equation by 5:
[tex]\[
x = \frac{15}{5}
\][/tex]
Simplify:
[tex]\[
x = 3
\][/tex]
So, the unknown number is [tex]\( \boxed{3} \)[/tex].
