Question

solve the inequality and graph the solutions.
\\( \frac { z } { 9 } \geq 4 \\)
\\( z \geq 36 \\)
\\( z \geq 4 / 9 \\)
\\( z \geq 36 \\)
\\( z \geq 36 \\)

Explanation:

Step1: Multiply both sides by 9

$$\frac{z}{9}\geq4$$
$$\frac{z}{9}\times9\geq4\times9$$

Step2: Simplify

$$z\geq36$$

For graphing \(z\geq36\), we use a closed - circle at \(36\) (because the inequality is \(\geq\), meaning \(36\) is included in the solution set) and draw an arrow to the right (since \(z\) is greater than or equal to \(36\)).

Answer:

\(z\geq36\) (the fourth option where there is a closed - circle at \(36\) and an arrow to the right)