Given the functions $f(x) = \frac{2x - 1}{2}$ and $g(x) = x - 4$, find the value of $x$ when $f(x) = 6$ and when $g(x) = 1$.

1. Problem Description

Given the functions $f(x) = \frac{2x - 1}{2}$ and $g(x) = x - 4$, find the value of $x$ when $f(x) = 6$ and when $g(x) = 1$.

2. Solution Steps

(a) Find $x$ if $f(x) = 6$.

We are given $f(x) = \frac{2x - 1}{2}$ and we want to find $x$ such that $f(x) = 6$.

So we set $\frac{2x - 1}{2} = 6$.

Multiply both sides by 2:

$2x - 1 = 12$

Add 1 to both sides:

$2x = 13$

Divide both sides by 2:

$x = \frac{13}{2}$

(b) Find $x$ if $g(x) = 1$.

We are given $g(x) = x - 4$ and we want to find $x$ such that $g(x) = 1$.

So we set $x - 4 = 1$.

Add 4 to both sides:

$x = 5$

3. Final Answer

(a) $x = \frac{13}{2}$

(b) $x = 5$