Question

ve and graph the following compound inequalities

1. ( 4x leq 48 ) or ( x - 9 geq 30 )

Explanation:

Step1: Solve \(4x \leq 48\)

Divide both sides by 4: \(x \leq \frac{48}{4}\)
\(x \leq 12\)

Step2: Solve \(x - 9 \geq 30\)

Add 9 to both sides: \(x \geq 30 + 9\)
\(x \geq 39\)

Step3: Combine the solutions

Since it's an "or" compound inequality, the solution is the union of the two solution sets. So \(x \leq 12\) or \(x \geq 39\).

Answer:

The solution to the compound inequality \(4x \leq 48\) or \(x - 9 \geq 30\) is \(x \leq 12\) or \(x \geq 39\). For graphing, we would have a number line with a closed circle at 12 and an arrow to the left, and a closed circle at 39 and an arrow to the right.