Question

1. which of the following graphs shows the solution set to 4x - 5 ≥ 3 or 5 - x > 8?

Explanation:

Step1: Solve the first inequality

Solve \(4x - 5\geq3\). Add 5 to both sides: \(4x-5 + 5\geq3 + 5\), which simplifies to \(4x\geq8\). Then divide both sides by 4: \(x\geq2\).

Step2: Solve the second inequality

Solve \(5 - x>8\). Subtract 5 from both sides: \(5 - x-5>8 - 5\), getting \(-x>3\). Multiply both sides by - 1 and reverse the inequality sign: \(x < - 3\).

Step3: Analyze the 'or' condition

The solution set for \(4x - 5\geq3\) or \(5 - x>8\) is the union of the solution sets of the two inequalities, which is \(x < - 3\) or \(x\geq2\). On a number - line, \(x < - 3\) has an open circle at - 3 and points to the left, and \(x\geq2\) has a closed circle at 2 and points to the right.

Answer:

The first graph (with an open circle at - 3 and a closed circle at 2, arrows pointing left from - 3 and right from 2)