Sure, let's go through the steps to solve for [tex]\( x \)[/tex] in the equation [tex]\( 8x - 10y = 4 \)[/tex].
1. Start with the given equation:
[tex]\[
8x - 10y = 4
\][/tex]
2. Isolate the term containing [tex]\( x \)[/tex] on one side. To do that, we can add [tex]\( 10y \)[/tex] to both sides of the equation to get:
[tex]\[
8x = 10y + 4
\][/tex]
3. Now, solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 8:
[tex]\[
x = \frac{10y + 4}{8}
\][/tex]
4. To simplify the expression, we can break it down:
[tex]\[
x = \frac{10y}{8} + \frac{4}{8}
\][/tex]
Simplifying the fractions, we get:
[tex]\[
x = \frac{5y}{4} + \frac{1}{2}
\][/tex]
5. To find the specific value of [tex]\( x \)[/tex], let's assume a particular value for [tex]\( y \)[/tex]. If we let [tex]\( y = 0 \)[/tex]:
[tex]\[
x = \frac{5 \cdot 0}{4} + \frac{1}{2}
\][/tex]
Simplifying this gives:
[tex]\[
x = \frac{1}{2}
\][/tex]
Therefore, when [tex]\( y = 0 \)[/tex], the value of [tex]\( x \)[/tex] is [tex]\( 0.5 \)[/tex].
