Question

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

Answer 1

SECOND graph.

Explanation:

Given compound inequality,

`x \leq (5)/(4)\text{ or }x \geq (5)/(2)`

`\because (5)/(4)=1.25\text{ or }(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