Question: Write a compound inequality for the graph shown below. Use x for your variable.

Write a compound inequality for the graph shown below. Use x for your variable.

Solution

The graph shows two distinct areas where the variable \( x \) is valid, using dots to indicate boundaries. 1. The left part of the graph shows a filled dot at \(-8\) and an open dot at \(-4\). - A filled dot at \(-8\) means it includes \(-8\): \( x \geq -8 \) - An open dot at \(-4\) means it does not include \(-4\): \( x < -4 \) Therefore, the left inequality is: \[ -8 \leq x < -4 \] 2. The right part of the graph shows a filled dot at \(2\) and an open dot at \(5\). - A filled dot at \(2\) means it includes \(2\): \( x \geq 2 \) - An open dot at \(5\) means it does not include \(5\): \( x < 5 \) Therefore, the right inequality is: \[ 2 \leq x < 5 \] 3. Combine these inequalities with “or” since the graph indicates two separate valid regions for \( x \). The compound inequality is: \[ \begin{cases} -8 \leq x < -4 & \\ 2 \leq x < 5 & \end{cases} \]