To solve the equation [tex]\( 5x + c = k \)[/tex] for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]. Here’s the step-by-step solution:
1. Start with the given equation:
[tex]\[
5x + c = k
\][/tex]
2. To isolate [tex]\( x \)[/tex], first, we need to get rid of the constant term [tex]\( c \)[/tex]. We do this by subtracting [tex]\( c \)[/tex] from both sides of the equation:
[tex]\[
5x + c - c = k - c
\][/tex]
Simplifying, we get:
[tex]\[
5x = k - c
\][/tex]
3. Now, to solve for [tex]\( x \)[/tex], we need to eliminate the coefficient of [tex]\( x \)[/tex], which is 5. We do this by dividing both sides of the equation by 5:
[tex]\[
\frac{5x}{5} = \frac{k - c}{5}
\][/tex]
Simplifying, we get:
[tex]\[
x = \frac{k - c}{5}
\][/tex]
4. So, the solution for [tex]\( x \)[/tex] is:
[tex]\[
x = \frac{k - c}{5}
\][/tex]
This matches with option A:
[tex]\[
A. \ x = \frac{k - c}{5}
\][/tex]
Therefore, the correct answer is option A.
