To solve the inequality \(-3y + 4 \geq 14\), we need to isolate \(y\). Let's go through the steps:
1. Subtract 4 from both sides of the inequality:
[tex]\[
-3y + 4 - 4 \geq 14 - 4
\][/tex]
[tex]\[
-3y \geq 10
\][/tex]
2. Divide both sides by -3, and remember to flip the inequality sign because we are dividing by a negative number:
[tex]\[
y \leq \frac{10}{-3}
\][/tex]
[tex]\[
y \leq -3.3333\ldots
\][/tex]
The solution to the inequality \( -3y + 4 \geq 14 \) is \( y \leq -3.3333\ldots \), which can be rounded to \( y \leq -3.33 \) (approximately).
### Graphing this solution:
When graphing the solution \( y \leq -3.33 \), you should:
- Plot a vertical line at \( y = -3.33 \) on the number line.
- Shade everything to the left of this line, indicating all the values less than or equal to \( -3.33 \).
- Use a closed circle (or solid line) at \( y = -3.33 \) to show that \(-3.33\) is included in the solution.
In the coordinate plane:
- You would shade the region to the left of the vertical line \( y = -3.33 \).
By following these steps, you create a graph that accurately represents the solution to the inequality.
