Certainly, let's tackle each of these equations step by step.
### 1) Solving [tex]\(\frac{1}{3} + \frac{x}{3} = 2\)[/tex]
1. Start with the equation:
[tex]\[
\frac{1}{3} + \frac{x}{3} = 2
\][/tex]
2. Combine the fractions on the left-hand side:
Since both terms have a common denominator of 3, we can combine them:
[tex]\[
\frac{1 + x}{3} = 2
\][/tex]
3. Eliminate the fraction by multiplying both sides by 3:
[tex]\[
1 + x = 6
\][/tex]
4. Isolate [tex]\( x \)[/tex] by subtracting 1 from both sides:
[tex]\[
x = 6 - 1
\][/tex]
5. Solution:
[tex]\[
x = 5
\][/tex]
So, the solution to the first equation is [tex]\( x = 5 \)[/tex].
### 9) Solving [tex]\( 5 = \frac{x}{1} = \frac{3}{4} \)[/tex]
There appears to be a typo in the given equation. The correct interpretation seems to be solving for [tex]\( x \)[/tex] given [tex]\( 5 = x \)[/tex]. Hence:
1. Start with the equation:
[tex]\[
5 = x
\][/tex]
2. Solution:
[tex]\[
x = 5
\][/tex]
So, the solution to this equation is [tex]\( x = 5 \)[/tex] as well.
### Summary
Both equations yield the same solution:
[tex]\[
x = 5
\][/tex]
