To solve for [tex]\( x \)[/tex] in the equation [tex]\( x + \frac{1}{3} = \frac{8}{9} \)[/tex], follow these steps:
1. Isolate [tex]\( x \)[/tex] on one side:
[tex]\[
x + \frac{1}{3} = \frac{8}{9}
\][/tex]
To isolate [tex]\( x \)[/tex], subtract [tex]\( \frac{1}{3} \)[/tex] from both sides:
[tex]\[
x = \frac{8}{9} - \frac{1}{3}
\][/tex]
2. Find a common denominator:
The fractions [tex]\( \frac{8}{9} \)[/tex] and [tex]\( \frac{1}{3} \)[/tex] need a common denominator to be subtracted. The common denominator for 9 and 3 is 9.
Convert [tex]\( \frac{1}{3} \)[/tex] to a fraction with a denominator of 9:
[tex]\[
\frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
\][/tex]
3. Subtract the fractions:
Now, subtract the two fractions:
[tex]\[
\frac{8}{9} - \frac{3}{9} = \frac{8 - 3}{9} = \frac{5}{9}
\][/tex]
Thus, the solution for [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{5}{9}
\][/tex]
So the correct answer is (B) [tex]\( x = \frac{5}{9} \)[/tex].
