4. Determine if each value is a solution of the inequality \( 3 \geq \frac{1}{3} y \)

To determine whether specific values of \( y \) satisfy the inequality: \[ 3 \geq \frac{1}{3}y \] we can solve the inequality for \( y \) and then evaluate each given value accordingly. Here's a step-by-step guide: ### Step 1: Solve the Inequality for \( y \) Start with the original inequality: \[ 3 \geq \frac{1}{3}y \] To isolate \( y \), multiply both sides of the inequality by \( 3 \) (which is positive, so the direction of the inequality remains the same): \[ 3 \times 3 \geq y \] \[ 9 \geq y \] This can be rewritten as: \[ y \leq 9 \] ### Step 2: Interpret the Solution The inequality \( y \leq 9 \) means that **any value of \( y \) that is less than or equal to 9** satisfies the original inequality \( 3 \geq \frac{1}{3}y \). Conversely, any value of \( y \) **greater than 9** does **not** satisfy the inequality. ### Step 3: Evaluate Specific Values Let's apply this to some example values of \( y \): 1. **\( y = 6 \)** \[ 3 \geq \frac{1}{3} \times 6 \implies 3 \geq 2 \] **Result:** True. \( 6 \leq 9 \), so \( y = 6 \) is a solution. 2. **\( y = 9 \)** \[ 3 \geq \frac{1}{3} \times 9 \implies 3 \geq 3 \] **Result:** True. \( 9 \leq 9 \), so \( y = 9 \) is a solution. 3. **\( y = 12 \)** \[ 3 \geq \frac{1}{3} \times 12 \implies 3 \geq 4 \] **Result:** False. \( 12 > 9 \), so \( y = 12 \) is **not** a solution. 4. **\( y = -3 \)** \[ 3 \geq \frac{1}{3} \times (-3) \implies 3 \geq -1 \] **Result:** True. \( -3 \leq 9 \), so \( y = -3 \) is a solution. ### Summary - **Values \( y \leq 9 \):** Satisfy the inequality \( 3 \geq \frac{1}{3}y \). - **Values \( y > 9 \):** Do **not** satisfy the inequality. If you have specific values you'd like to check, substitute them into the inequality using the method above to determine if they are solutions.