Answer:
[tex]\frac{x}{2}<1\textrm{ or }\frac{4x-2}{2}\geq 13[/tex]
Step-by-step explanation:
From the graph, we can conclude that,
[tex]x[/tex] is less than 2 and not including as there is a hollow circle at the mark 2.
Also, [tex]x[/tex] 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 [tex]x<2\textrm{ or }x\geq 7[/tex]
Now, the option that simplifies to the above inequality is the required answer.
Let us check the first option.
[tex]\frac{x}{2}<1\textrm{ or }\frac{4x-2}{2}\geq 13[/tex]
[tex]\frac{x}{2}<1\\\frac{x}{2}\times 2<1\times 2\\x<2\\\\\frac{4x-2}{2}\geq 13\\\frac{4x-2}{2}\times 2\geq 13\times 2\\4x-2\geq 26\\4x\geq 26+2\\4x\geq 28\\x\geq \frac{28}{4}\\x\geq 7[/tex]
Therefore, option 1 simplifies to the above compound inequality.
So, the correct answer is option 1.
