Question

What graph represents the compound inequality x<5/4 or x>5/2

Answer 1

Answer:

SECOND graph.

Step-by-step explanation:

Given compound inequality,

$x \leq \frac{5}{4}\text{ or }x \geq \frac{5}{2}$

$\because \frac{5}{4}=1.25\text{ or }\frac{5}{2}=2.5$

$\implies x \leq 1.25\text{ or }x\geq 2.5$

If x ≥ 1.25

In the number line closed circle on 1.25 and shaded left side from 1.25,

If x ≤ 2.5

In the number line closed circle on 2.5 and shaded right side from 2.5

Hence, SECOND option is correct.

Answer 2

For this case we have to:

$x \leq \frac {5} {4}$: Represents all values less than or equal to$\frac {5} {4}.$

$x \geq \frac {5} {2}$: Represents all values greater than or equal to $\frac {5} {2}.$

As the inequalities include the sign "=", then the borders of the graphs will be closed.

$\frac {5} {4} = 1.25\\\frac {5} {2} = 2.5$

The word "or" indicates one solution or the other, so the correct option is graph B

ANswer:

Option B