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The set of all real values of $x$ for which $(x^2 - |x + 9| + x) > 0$, is

The number of distinct integer solutions $(x, y)$ of the equation $|x + y| + |x - y| = 2$, is

The number of distinct real values of x, satisfying the equation.

max {x, 2} - min {x, 2} $= |x + 2| - |x − 2|$, is

If x and y are real numbers such that $|x| + x + y = 15$ and $x + |y| - y = 20$, then $(x - y)$ equals

The area of the quadrilateral bounded by the $Y$-axis, the line $x=5$, and the lines $|x-y|-|x-5|=2$, is

The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is

The largest real value of a for which the equation $|x + a| + |x - 1| = 2$ has an infinite number of solutions for $x$ is

Let $0 \leq a \leq x \leq 100$ and $f(x)=|x-a|+|x-100|+|x-a-50|$. Then the maximum value of $f(x)$ becomes $100$ when $a$ is equal to

If $3x + 2|y|+ y = 7$ and $x + |x|+ 3y = 1$, then $x + 2y$ is

For a real number x the condition $|3x - 20| + |3x - 40| = 20$ necessarily holds if

If r a constant such that $|x^2 - 4x - 13| = r$ has exactly three distinct real roots, then the value of r is

The area, in sq. units, enclosed by the lines $x = 2$, $y = |x - 2| + 4$, the $X-$axis and the $Y-$axis is equal to

In how many ways can a pair of integers $(x, a)$ be chosen such that $x^2 - 2 | x | + | a - 2 | = 0$?

The number of solution to the equation $|x|(6x^2 + 1) = 5x^2$ is

The product of the distinct roots of $|x^2 − x − 6| = x + 2$ is

Let $S$ be the set of all points $(x, y)$ in the x-y plane such that $|x|+|y| \le 2$ and $|x| \ge 1$. Then, the area, in square units, of the region represented by $S$ equals:

Let $f(x) = 2x – 5$ and $g(x) = 7 – 2x$. Then $|f(x) + g(x)| = |f(x)| + |g(x)|$ if and only if

The area of the closed region bounded by the equation $| x | + | y | = 2$ in the two-dimensional plane is

The shortest distance of the point $\left(\frac{1}{2}, 1\right)$ from the curve $y=|x-1|+|x+1|$ is