Question

which graphs represents the compound inequality $xleq \frac{5}{4}$ or $xgeq \frac{5}{2}$? -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 $x\leq\frac{5}{4}$

On a number - line, $\frac{5}{4}=1.25$, and the graph of $x\leq1.25$ has a closed - circle at $1.25$ and an arrow pointing to the left.

Step2: Analyze $x\geq\frac{5}{2}$

On a number - line, $\frac{5}{2}=2.5$, and the graph of $x\geq2.5$ has 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 the solution set includes all values of $x$ that satisfy either of the inequalities.

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 $x\geq\frac{5}{2}$.