Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

Solve the inequality $\frac{t-1}{4t+5} < \frac{t-3}{4t-3}$.

InequalitiesRational InequalitiesInterval AnalysisAlgebraic Manipulation

The problem asks to calculate the determinants of the following 2x2 matrices: a) $\begin{vmatrix} 1 ...

Linear AlgebraDeterminantsMatrices

We are asked to solve the equation: $\frac{2x-6}{x-1} - \frac{x+2}{x+1} = \frac{3x+4}{x^2+x-2}$.

EquationsRational EquationsQuadratic FormulaSolving Equations

We need to solve the inequality $\frac{(x+1)|x-2|}{x^2+2} < -1$.

InequalitiesAbsolute ValueCase Analysis

We need to solve the inequality $|\frac{3x}{2x+3}| < 2$.

InequalitiesAbsolute ValueRational Expressions

The problem asks us to solve two inequalities for $n$. The first inequality is $\frac{n-1}{n+1} < 5$...

InequalitiesRational InequalitiesInterval Notation

We are asked to solve the inequality $\frac{|x-1|}{x} < 1$.

InequalitiesAbsolute ValueAlgebraic ManipulationCase AnalysisInterval Notation

Solve the system of equations: $|2x-1|-y=2$ $x-|4-y|=-1$

Absolute ValueSystems of EquationsCase Analysis

We are given a system of two equations with two variables, $x$ and $y$. The equations are: $x - 2 = ...

Linear EquationsSystem of EquationsSolving Equations

We are asked to simplify the expression $y = \frac{|x+1| - |x-1|}{2}$.

Absolute ValuePiecewise FunctionSimplificationCasework

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