Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem asks us to solve the equation $\frac{2}{x-1} = \frac{3}{x-2}$ for $x$. We must also cons...
EquationsRational EquationsSolving EquationsExtraneous Solutions
2025/3/21
The problem defines a piecewise function $f(x)$. $f(x) = x^2 + 1$ if $x < 1$ and $f(x) = 3x - 1$ if ...
Piecewise FunctionsFunction Evaluation
2025/3/21
We need to find the solution to the inequality $4x - 1 > 3(x + 2) - 4$. The answer should be in inte...
InequalitiesLinear InequalitiesInterval NotationAlgebraic Manipulation
2025/3/21
Find the domain of the function $f(x) = \sqrt{2x + 4}$.
FunctionsDomainSquare RootInequalities
2025/3/21
Find the equation of the line passing through the point $(-1, 2)$ and perpendicular to the line $y =...
Linear EquationsSlopePerpendicular LinesPoint-Slope Form
2025/3/21
The problem asks us to find the slope $m$ and y-intercept $b$ of the line given by the equation $3x ...
Linear EquationsSlope-intercept formEquation of a line
2025/3/21
The problem asks to subtract the polynomial $(-9m^3 + 9m + 3.4)$ from the polynomial $(7m^3 + 8m^2 -...
PolynomialsSubtractionSimplificationCombining Like Terms
2025/3/21
The problem asks us to add the following polynomials: $(x^2 + 8x - 7) + (-4x^2 - 2x + 1) + (x^2 - x ...
PolynomialsAlgebraic ExpressionsSimplification
2025/3/21
The problem involves two quadratic functions $f(x) = -2x^2$ and $g(x) = x^2 + ax + b$. We are given...
Quadratic FunctionsParabolasVertex of a ParabolaCompleting the SquareQuadratic EquationsFinding Minimum/Maximum ValuesSolving Equations
2025/3/21
$1222 is divided among $2X$, $6Y$, and $8Z$ such that the shares of $X$, $Y$, and $Z$ are in the rat...
Ratio and ProportionLinear EquationsWord Problem
2025/3/21