To solve the inequality [tex]\(-9.5 + 6x \geq 42.1\)[/tex] and express the solution in interval notation, follow these steps:
1. Isolate the term involving [tex]\( x \)[/tex]:
Begin by adding 9.5 to both sides of the inequality to isolate the term involving [tex]\( x \)[/tex].
[tex]\[
-9.5 + 6x + 9.5 \geq 42.1 + 9.5
\][/tex]
Simplifying this, we get:
[tex]\[
6x \geq 51.6
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
Next, divide both sides of the inequality by 6 to solve for [tex]\( x \)[/tex]:
[tex]\[
\frac{6x}{6} \geq \frac{51.6}{6}
\][/tex]
Simplifying this, we find:
[tex]\[
x \geq 8.6
\][/tex]
3. Express the solution in interval notation:
The solution [tex]\( x \geq 8.6 \)[/tex] means that [tex]\( x \)[/tex] can be any number greater than or equal to 8.6. In interval notation, this is represented as:
[tex]\[
[8.6, \infty)
\][/tex]
Thus, the correct interval notation that represents the solution of [tex]\(-9.5 + 6x \geq 42.1\)[/tex] is [tex]\([8.6, \infty)\)[/tex]. Therefore, the correct choice among the given options is:
[tex]\[
[8.6, \infty)
\][/tex]
