Alright, let's find the [tex]\(x\)[/tex]-intercept of the equation [tex]\(-6x + 3y = 8\)[/tex].
To find the [tex]\(x\)[/tex]-intercept, we need to set [tex]\(y = 0\)[/tex] and solve for [tex]\(x\)[/tex]. Let's break down the steps:
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
-6x + 3(0) = 8
\][/tex]
2. Simplify the equation:
[tex]\[
-6x = 8
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by [tex]\(-6\)[/tex]:
[tex]\[
x = \frac{8}{-6}
\][/tex]
4. Simplify the fraction:
[tex]\[
x = -\frac{4}{3}
\][/tex]
Thus, the [tex]\(x\)[/tex]-intercept of the equation [tex]\(-6x + 3y = 8\)[/tex] is [tex]\(-\frac{4}{3}\)[/tex]. In decimal form, this is approximately [tex]\(-1.3333333333333333\)[/tex].
