Questions: Solve each inequality, graph the solution on the number line, and interval notation. -2 y ≥ -8/5 a) Solve the inequality Inequality notation solution Contradiction (no solution) Identity (all real numbers) b) Graph the solution on the number line. c) Write in interval notation Interval notation solution: No solution

Solution Steps

Given the inequality: \[ -2y \geq \frac{8}{5} \]

First, divide both sides by -2. Remember that dividing by a negative number reverses the inequality sign: \[ y \leq -\frac{8}{5 \times 2} \] \[ y \leq -\frac{8}{10} \] \[ y \leq -\frac{4}{5} \]

To graph \( y \leq -\frac{4}{5} \) on the number line:

• Place a closed dot at \( -\frac{4}{5} \) to indicate that \( y \) can be equal to \( -\frac{4}{5} \).
• Shade the number line to the left of \( -\frac{4}{5} \) to indicate all values less than \( -\frac{4}{5} \).

The interval notation for \( y \leq -\frac{4}{5} \) is: \[ (-\infty, -\frac{4}{5}] \]

Final Answer