Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem requires solving the inequality $|x+1| \ge 2|x+2|$. Additionally, there is an expression...
InequalitiesAbsolute ValueCase Analysis
2025/5/26
Solve the given equation for $x$ and then determine the real number $m$ such that $|x| < 1$. The equ...
EquationsInequalitiesAbsolute ValueRational Expressions
2025/5/26
The problem is to solve the equation $\frac{2m-5}{(m-1)(x+2)} - \frac{3}{x+1} = \frac{3x+4}{x^2+3x+2...
Algebraic EquationsSolving EquationsRational ExpressionsSimplificationVariable Isolation
2025/5/26
The problem asks to draw the graphs of several piecewise-defined functions. We will focus on functio...
Piecewise FunctionsGraphingLinear Functions
2025/5/26
Solve the inequality $|\frac{-6x}{x^2+9}| > 1$.
InequalitiesAbsolute ValueQuadratic InequalitiesNo Solution
2025/5/26
We are given a system of equations involving absolute values: $|x| + |y-1| = 1$ $x + 2y = 3$
Absolute Value EquationsSystems of EquationsCase Analysis
2025/5/26
We are given a system of three linear equations with three unknowns $x$, $y$, and $z$. The system is...
Linear EquationsSystems of EquationsSolving EquationsVariables
2025/5/26
We need to solve the inequality $\frac{x}{a} + \frac{1-3x}{2} < \frac{x+2}{4a}$, given that $a \neq ...
InequalitiesLinear InequalitiesCase AnalysisVariable Coefficient
2025/5/26
We are given a system of two linear equations with two variables $x$ and $y$, and a parameter $m$: $...
Linear EquationsSystems of EquationsInequalitiesParameterSolution Sets
2025/5/26
We are given a system of two linear equations with two variables $x$ and $y$: $(m+1)x - my = 4$ $3x ...
Linear EquationsSystems of EquationsSolving EquationsSubstitution Method
2025/5/26