Let's solve each equation step-by-step:
### Problem (a)
Equation: [tex]\(\frac{x}{3} - 2 = 6\)[/tex]
1. To isolate the term containing [tex]\( x \)[/tex], we first add 2 to both sides of the equation.
[tex]\[
\frac{x}{3} - 2 + 2 = 6 + 2
\][/tex]
This simplifies to:
[tex]\[
\frac{x}{3} = 8
\][/tex]
2. Next, to solve for [tex]\( x \)[/tex], we multiply both sides of the equation by 3.
[tex]\[
\left(\frac{x}{3}\right) \times 3 = 8 \times 3
\][/tex]
This simplifies to:
[tex]\[
x = 24
\][/tex]
So, the solution for part (a) is:
[tex]\[
x = 24
\][/tex]
### Problem (b)
Equation: [tex]\(\frac{x}{5} + 1 = 5\)[/tex]
1. To isolate the term containing [tex]\( x \)[/tex], we first subtract 1 from both sides of the equation.
[tex]\[
\frac{x}{5} + 1 - 1 = 5 - 1
\][/tex]
This simplifies to:
[tex]\[
\frac{x}{5} = 4
\][/tex]
2. Next, to solve for [tex]\( x \)[/tex], we multiply both sides of the equation by 5.
[tex]\[
\left(\frac{x}{5}\right) \times 5 = 4 \times 5
\][/tex]
This simplifies to:
[tex]\[
x = 20
\][/tex]
So, the solution for part (b) is:
[tex]\[
x = 20
\][/tex]
### Summary
- The value of [tex]\( x \)[/tex] in part (a) is [tex]\( 24 \)[/tex].
- The value of [tex]\( x \)[/tex] in part (b) is [tex]\( 20 \)[/tex].
