Of course! Let's solve the inequality step-by-step:
Given the inequality:
[tex]\[ 23 + 6y > 5 \][/tex]
1. Isolate the term containing [tex]\( y \)[/tex]:
We'll start by subtracting 23 from both sides to get the term with [tex]\( y \)[/tex] by itself on one side of the inequality.
[tex]\[
23 + 6y - 23 > 5 - 23
\][/tex]
Simplifying this, we have:
[tex]\[
6y > -18
\][/tex]
2. Solve for [tex]\( y \)[/tex]:
Next, we'll divide both sides of the inequality by 6 to solve for [tex]\( y \)[/tex]. Since 6 is positive, the direction of the inequality will remain the same.
[tex]\[
y > \frac{-18}{6}
\][/tex]
Simplifying the fraction:
[tex]\[
y > -3
\][/tex]
Therefore, the solution to the inequality [tex]\( 23 + 6y > 5 \)[/tex] is:
[tex]\[ y > -3 \][/tex]
In interval notation, this can be written as:
[tex]\[ (-3, \infty) \][/tex]
This means that [tex]\( y \)[/tex] must be greater than [tex]\(-3\)[/tex], but it has no upper limit (it can be any number greater than [tex]\(-3\)[/tex]).
