Algebra
Problems related to equations, functions, polynomials, etc.
Problems in this category
The problem states that the mean proportional between $x$ and $272$ is $68$. We need to find the val...
Mean ProportionalEquations
2025/7/10
Given $x - \frac{1}{x} = 4$, find the value of $x^3 - \frac{1}{x^3}$.
Algebraic ManipulationIdentitiesPolynomials
2025/7/10
The problem is to solve the inequality $(\frac{1}{2})^x < 8$ for $x$.
InequalitiesExponentsLogarithms
2025/7/9
We need to solve the equation $\frac{3}{x+7} - \frac{1}{x+2} = 0$.
EquationsRational EquationsSolving Equations
2025/7/8
There are 120 students in a test, and their average score is 70. The average score of the passed stu...
Word ProblemAverageLinear Equations
2025/7/8
The problem gives us a recursive formula for a sequence $U_n$: $U_1 = 7$ $U_n = 3U_{n-1} + 2n$ for $...
Sequences and SeriesRecurrence Relations
2025/7/8
The problem is to solve the equation $\frac{2x}{x-5} = \frac{2}{3}$ for $x$.
EquationsLinear EquationsSolving EquationsRational Equations
2025/7/7
Solve the equation $\frac{2x}{x-5} = \frac{2}{3}$ for $x$.
Linear EquationsEquation SolvingFractions
2025/7/7
The problem consists of several math questions. I will answer the following questions: 1. i) If $\s...
SimplificationNumber Base ConversionQuadratic EquationsRadicalsAlgebraic Manipulation
2025/7/7
The problem is to analyze the inequality $4x^2 + 8xy + 3y^2 > 0$. We want to determine the condition...
InequalitiesQuadratic ExpressionsFactoringLinear Inequalities2D Geometry
2025/7/7