To solve for [tex]\( x \)[/tex] in the equation [tex]\( z = 7x - y \)[/tex], we need to isolate [tex]\( x \)[/tex]. Follow these steps:
1. Start with the given equation:
[tex]\[
z = 7x - y
\][/tex]
2. To isolate [tex]\( x \)[/tex], first add [tex]\( y \)[/tex] to both sides of the equation:
[tex]\[
z + y = 7x
\][/tex]
3. Next, divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{z + y}{7}
\][/tex]
Now, suppose we are given specific values for [tex]\( z \)[/tex] and [tex]\( y \)[/tex]. For demonstration purposes, let's take [tex]\( z = 14 \)[/tex] and [tex]\( y = 7 \)[/tex].
4. Substitute these values into the equation:
[tex]\[
x = \frac{14 + 7}{7}
\][/tex]
5. Simplify the expression inside the fraction:
[tex]\[
x = \frac{21}{7}
\][/tex]
6. Finally, perform the division:
[tex]\[
x = 3
\][/tex]
Therefore, the solution for [tex]\( x \)[/tex] is:
[tex]\[
x = 3
\][/tex]
