Discover published sets by community

An inequality involving a linear expression in one variable without exponents, such as $3x - 1 > 2$.

An inequality containing a polynomial, such as $x^2 - 4x + 3 < 0$.

An inequality involving the absolute value, such as $|2x + 1| > 3$. It requires considering both the positive and negative scenarios of the expression inside the absolute value.

An inequality containing a ratio of polynomials, such as $\frac{x-1}{x+2} \leq 0$. Critical points from the numerator and denominator are used to find the solution set.

A set of two or more linear inequalities in the same variables, such as $\begin{cases} y > 2x + 1 \\ y \leq -x + 3 \end{cases}$.

An inequality involving a quadratic expression, for example, $x^2 - x - 6 > 0$.

A fundamental inequality in geometry stating that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side, such as $a + b > c$ for the sides of a triangle.

An inequality that combines two or more simple inequalities using the words 'and' or 'or', for example, $3 < x + 1 < 5$ means $x$ can take on values between $2$ and $4$.

An inequality containing an exponential function, such as $2^x < 8$.

An inequality involving logarithmic functions, like $\log(x) > 1$.

An inequality akin to the equation of an ellipse but with an inequality sign. For example, $\frac{x^2}{a^2} + \frac{y^2}{b^2} < 1$ represents the points inside an ellipse.

An inequality involving trigonometric functions, such as $\sin x > 0.5$.

An inequality related to hyperbolas, similar to a hyperbolic equation, for example, $\frac{x^2}{a^2} - \frac{y^2}{b^2} > 1$, which indicates the region outside the hyperbola.

An inequality defined by different expressions depending on the interval the variable lies in, such as $f(x) = \begin{cases} x^2, & x \leq 0 \\ -x, & x > 0 \end{cases}$, then solving for $f(x) < 1$.