To solve the problem where one-third of a number decreased by six equals eight, we can follow these steps:
1. Let's represent the unknown number by [tex]\( x \)[/tex].
2. According to the problem, one-third of this number decreased by six equals eight. Mathematically, we can express this as:
[tex]\[
\frac{1}{3}x - 6 = 8
\][/tex]
3. Next, we need to isolate [tex]\( x \)[/tex]. First, we should get rid of the -6 on the left side by adding 6 to both sides of the equation:
[tex]\[
\frac{1}{3}x - 6 + 6 = 8 + 6
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{1}{3}x = 14
\][/tex]
4. Now, to solve for [tex]\( x \)[/tex], we need to eliminate the one-third coefficient. We can do this by multiplying both sides of the equation by 3:
[tex]\[
3 \times \frac{1}{3}x = 14 \times 3
\][/tex]
Simplifying this, we get:
[tex]\[
x = 42
\][/tex]
Therefore, the number is [tex]\( 42 \)[/tex].
Out of the options given: 14, 24, and 42, the correct answer is:
O 42
