Given: A value of x as-
[tex]x=\frac{7}{4}[/tex]
Required: To determine the position of the given x value with respect to the line-
[tex]x=-\frac{3}{2}[/tex]
Explanation: A function's absolute value always gives a positive value.
So for the given x value, we have
[tex]\begin{gathered} x=\frac{7}{4} \\ \Rightarrow\lvert{x}\rvert=\frac{7}{4} \end{gathered}[/tex]
Since the given x is a positive real number, it will not be affected by the modulus function.
Now, x=a is a vertical line parallel to the y-axis and at 'a' distance from it.
Therefore the graph of both lines are
The red graph represents the graph of x=7/4 while the green line represents the line x=-3/2.
The distance of green line from y-axis is-
[tex]x=-1.5[/tex]
Similarly red line is at -
[tex]x=1.75[/tex]
Since,
[tex]\lvert{-1.5}\rvert<\lvert{1.75}\rvert[/tex]
We see that line x=7/4 is further from the y-axis than line x=-3/2.
Final Answer: Option C is correct.
