Sure, let's work through each inequality step by step to solve for [tex]\( y \)[/tex].
### Inequality #2: [tex]\( x - 5y \leq -20 \)[/tex]
1. Start with the inequality:
[tex]\[
x - 5y \leq -20
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex] by subtracting [tex]\( x \)[/tex] from both sides:
[tex]\[
-5y \leq -20 - x
\][/tex]
3. To solve for [tex]\( y \)[/tex], divide both sides by [tex]\(-5\)[/tex]. Remember that when you divide or multiply by a negative number, the inequality sign flips:
[tex]\[
y \geq \frac{-20 - x}{-5}
\][/tex]
4. Simplify the expression on the right-hand side:
[tex]\[
y \geq \frac{20 + x}{5}
\][/tex]
So, the simplified form of Inequality #2 is:
[tex]\[
y \geq \frac{20 + x}{5}
\][/tex]
### Inequality #1: [tex]\( 11x - 5y < 30 \)[/tex]
1. Start with the inequality:
[tex]\[
11x - 5y < 30
\][/tex]
2. Isolate the term involving [tex]\( y \)[/tex] by subtracting [tex]\( 11x \)[/tex] from both sides:
[tex]\[
-5y < 30 - 11x
\][/tex]
3. To solve for [tex]\( y \)[/tex], divide both sides by [tex]\(-5\)[/tex]. Remember that when you divide or multiply by a negative number, the inequality sign flips:
[tex]\[
y > \frac{30 - 11x}{-5}
\][/tex]
4. Simplify the expression on the right-hand side:
[tex]\[
y > \frac{11x - 30}{5}
\][/tex]
So, the simplified form of Inequality #1 is:
[tex]\[
y > \frac{11x - 30}{5}
\][/tex]
### Summary:
- The simplified inequality for [tex]\( x - 5y \leq -20 \)[/tex] when solved for [tex]\( y \)[/tex] is:
[tex]\[
y \geq \frac{20 + x}{5}
\][/tex]
- The simplified inequality for [tex]\( 11x - 5y < 30 \)[/tex] when solved for [tex]\( y \)[/tex] is:
[tex]\[
y > \frac{11x - 30}{5}
\][/tex]
