Step-by-step explanation:
To solve this inequality, let's simplify it step by step.
First, distribute the 6:
\[30 \geq 6 \times \left(\frac{2}{3}z + \frac{1}{3}\right)\]
\[30 \geq 4z + 2\]
Next, subtract 2 from both sides:
\[28 \geq 4z\]
Now, divide both sides by 4:
\[7 \geq z\]
So, the inequality is satisfied when \(z\) is less than or equal to 7.
