Question

which graphs represents the compound inequality x ≤ 5/4 or x ≥ 5/2? -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Explanation:

Step1: Analyze \(x\leq\frac{5}{4}\)

The inequality \(x\leq\frac{5}{4}=1.25\) represents all real - numbers less than or equal to \(1.25\). On a number line, it is represented by a closed - circle at \(1.25\) and an arrow pointing to the left.

Step2: Analyze \(x\geq\frac{5}{2}\)

The inequality \(x\geq\frac{5}{2} = 2.5\) represents all real - numbers greater than or equal to \(2.5\). On a number line, it is represented by a closed - circle at \(2.5\) and an arrow pointing to the right.

Step3: Consider the 'or' condition

The compound inequality \(x\leq\frac{5}{4}\) or \(x\geq\frac{5}{2}\) means that either \(x\) satisfies \(x\leq1.25\) or \(x\) satisfies \(x\geq2.5\).

Answer:

The second graph (the one with a closed - circle at \(1.25\) with an arrow to the left and a closed - circle at \(2.5\) with an arrow to the right) represents the compound inequality \(x\leq\frac{5}{4}\) or \(x\geq\frac{5}{2}\).