Alright, let's solve each of these equations step-by-step.
### 2) [tex]\( x + \frac{2}{7} = \frac{4}{7} \)[/tex]
1. Start with the equation:
[tex]\[
x + \frac{2}{7} = \frac{4}{7}
\][/tex]
2. To isolate [tex]\( x \)[/tex], subtract [tex]\(\frac{2}{7}\)[/tex] from both sides of the equation:
[tex]\[
x + \frac{2}{7} - \frac{2}{7} = \frac{4}{7} - \frac{2}{7}
\][/tex]
3. Simplify both sides:
[tex]\[
x = \frac{4}{7} - \frac{2}{7}
\][/tex]
4. Since the denominators are the same, subtract the numerators:
[tex]\[
x = \frac{4 - 2}{7}
\][/tex]
5. This results in:
[tex]\[
x = \frac{2}{7}
\][/tex]
So, the solution for this equation is:
[tex]\[
x = \frac{2}{7} = 0.2857142857142857
\][/tex]
### 3) [tex]\( x - \frac{1}{6} = \frac{11}{6} \)[/tex]
1. Start with the equation:
[tex]\[
x - \frac{1}{6} = \frac{11}{6}
\][/tex]
2. To isolate [tex]\( x \)[/tex], add [tex]\(\frac{1}{6}\)[/tex] to both sides of the equation:
[tex]\[
x - \frac{1}{6} + \frac{1}{6} = \frac{11}{6} + \frac{1}{6}
\][/tex]
3. Simplify both sides:
[tex]\[
x = \frac{11}{6} + \frac{1}{6}
\][/tex]
4. Since the denominators are the same, add the numerators:
[tex]\[
x = \frac{11 + 1}{6}
\][/tex]
5. This results in:
[tex]\[
x = \frac{12}{6}
\][/tex]
6. Simplify the fraction:
[tex]\[
x = 2
\][/tex]
So, the solution for this equation is:
[tex]\[
x = 2
\][/tex]
In summary, the solutions for the given equations are:
[tex]\[
\text{2) } x = 0.2857142857142857
\][/tex]
[tex]\[
\text{3) } x = 2
\][/tex]
