Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

The problem asks us to solve two inequalities for $x$ and fill in the boxes with the solution. (1) $...

InequalitiesLinear InequalitiesSolving InequalitiesAlgebraic Manipulation
2025/6/26

The problem asks to simplify the nested radicals (double square roots). Specifically, it asks to fin...

RadicalsSimplificationNested Radicals
2025/6/26

We are given that $a < b$. We need to determine the correct inequality sign (either $<$ or $>$) to f...

InequalitiesAlgebraic Manipulation
2025/6/26

The problem asks us to find the integer part $a$ and the fractional part $b$ of the number $\frac{2}...

RadicalsRationalizationSimplificationInteger PartFractional Part
2025/6/26

Given $x = \frac{1}{\sqrt{5}-\sqrt{3}}$ and $y = \frac{1}{\sqrt{5}+\sqrt{3}}$, we need to find the v...

Algebraic ManipulationRationalizationExponentsSimplificationSurds
2025/6/26

The problem asks us to rationalize the denominators of two expressions and choose the correct answer...

RationalizationRadicalsSimplificationExponents
2025/6/26

The problem asks us to evaluate four expressions and choose the correct answer from a set of options...

SimplificationRadicalsExponentsAlgebraic Expressions
2025/6/26

We are asked to find the values of the given expressions involving absolute values and radicals, and...

Absolute ValueRadicalsExpressionsSimplification
2025/6/26

We need to solve the following equations for $x$: 28. $\frac{4}{x+1} = \frac{7}{3x-2}$ 29. $\frac{x+...

Linear EquationsSolving EquationsFractional Equations
2025/6/25

We are asked to solve the following equations: 28. $\frac{4}{x+1} = \frac{7}{3x-2}$ 29. $\frac{x+1}{...

Linear EquationsSolving EquationsFractionsAlgebraic Manipulation
2025/6/25