Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
We are asked to solve the following equation for $x$: $a(x - \frac{1}{a^2}) + a^2(x - \frac{1}{a}) =...
Equation SolvingLinear EquationsVariable ManipulationSimplification
2025/5/25
The problem asks us to solve the linear equation $10 + 3(x - 2) = mx + 3$ for $x$, where $m$ is a re...
Linear EquationsSolving EquationsParameterEquation with Parameter
2025/5/25
The problem is to solve the linear equation $\frac{4x}{3} - \frac{2x-4}{3} + \frac{\frac{3x-5}{4} - ...
Linear EquationsEquation SolvingSimplificationFractions
2025/5/25
Solve for $x$ in the equation $\frac{\frac{1}{\sqrt{2}} - \frac{1}{\sqrt{5}}}{\frac{1}{\sqrt{2}} + \...
EquationsSimplificationRadicalsRationalization
2025/5/25
Solve the following two absolute value equations: g) $|x-1| + |x-2| + |x-3| = 18$ i) $2 + |x-6| = |x...
Absolute Value EquationsPiecewise FunctionsSolving EquationsInequalities
2025/5/25
We need to solve the equation $|x-2| + |x-3| + 2|x-4| = 9$.
Absolute Value EquationsCase Analysis
2025/5/25
We are given two absolute value equations to solve: c) $|x-1| - |x+5| = 6$ f) $||x-6|-8| = 10$
Absolute Value EquationsInequalitiesCase Analysis
2025/5/25
We need to solve the following equation for $y$: $\frac{1}{15y-10} - \frac{5-y}{27y^3 - 54y^2 + 36y ...
Equation SolvingRational EquationsPolynomial Factorization
2025/5/25
We need to solve the following equation for $y$: $\frac{y+1}{2y-1} - \frac{11y+5}{12(2y-1)} = \frac{...
EquationsRational EquationsSolving EquationsDomainVariable
2025/5/25
The problem is to solve the following equation for $y$: $\frac{4y-1}{y-4} - \frac{5y}{3y-12} - \frac...
EquationsRational ExpressionsSolving EquationsAlgebraic Manipulation
2025/5/25