Question

graphing compound inequalities
which graphs represents the compound inequality x ≤ 5/4 or x ≥ 5/2?

Explanation:

Step1: Analyze the first inequality

The inequality $x\leq\frac{5}{4}=1.25$ includes all values of $x$ that are less than or equal to $1.25$. On a number - line, this is represented by a closed - circle at $1.25$ (because of the $\leq$ sign) and an arrow pointing to the left.

Step2: Analyze the second inequality

The inequality $x\geq\frac{5}{2}=2.5$ includes all values of $x$ that are greater than or equal to $2.5$. On a number - line, this is represented by a closed - circle at $2.5$ (because of the $\geq$ sign) and an arrow pointing to the right.

Step3: Combine the two inequalities

The compound inequality $x\leq\frac{5}{4}$ or $x\geq\frac{5}{2}$ means that the solution set includes all values that satisfy either of the two inequalities.

Answer:

The second graph (from the top) represents the compound inequality $x\leq\frac{5}{4}$ or $x\geq\frac{5}{2}$ since it has 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.