Sure, let's solve this step-by-step. We need to find an unknown number [tex]\( x \)[/tex] such that one third of this number is 8 less than three times the number.
1. Define the unknown number: Let the unknown number be [tex]\( x \)[/tex].
2. Set up the equation:
The problem states that one third of the number is 8 less than three times the number. This can be written in mathematical terms as:
[tex]\[
\frac{x}{3} = 3x - 8
\][/tex]
3. Solve the equation:
To isolate [tex]\( x \)[/tex], we first eliminate the fraction by multiplying both sides by 3:
[tex]\[
x = 3 \cdot (3x - 8)
\][/tex]
Distribute the 3 on the right-hand side:
[tex]\[
x = 9x - 24
\][/tex]
To isolate [tex]\( x \)[/tex], we move all terms involving [tex]\( x \)[/tex] to one side. Subtract 9x from both sides:
[tex]\[
x - 9x = -24
\][/tex]
Simplify the left side:
[tex]\[
-8x = -24
\][/tex]
Divide both sides by -8:
[tex]\[
x = \frac{-24}{-8}
\][/tex]
Simplify the result:
[tex]\[
x = 3
\][/tex]
4. Verify the solution:
We can verify our solution by substituting [tex]\( x = 3 \)[/tex] back into the original condition of the problem.
- One third of the number [tex]\( x = 3 \)[/tex] is:
[tex]\[
\frac{3}{3} = 1
\][/tex]
- Three times the number minus 8 is:
[tex]\[
3 \times 3 - 8 = 9 - 8 = 1
\][/tex]
Both sides of the equation are equal, confirming our solution is correct.
Therefore, the unknown number is [tex]\( \boxed{3} \)[/tex].
