Question

HELP MEEE!! Please evaluating a compound. Inequality using a graph

Answer 1

`(x)/(2)<1\textrm{ or }(4x-2)/(2)\geq 13`

Explanation:

From the graph, we can conclude that,

`x` is less than 2 and not including as there is a hollow circle at the mark 2.

Also,
`x` is greater than or equal to 7 including 7 as there is a solid circle at the mark 7

So, the compound inequality will be
`x<2\textrm{ or }x\geq 7`

Now, the option that simplifies to the above inequality is the required answer.

Let us check the first option.

`(x)/(2)<1\textrm{ or }(4x-2)/(2)\geq 13`

`(x)/(2)<1\\(x)/(2)* 2<1* 2\\x<2\\\\(4x-2)/(2)\geq 13\\(4x-2)/(2)* 2\geq 13* 2\\4x-2\geq 26\\4x\geq 26+2\\4x\geq 28\\x\geq (28)/(4)\\x\geq 7`

Therefore, option 1 simplifies to the above compound inequality.

So, the correct answer is option 1.