Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are asked to solve several equations. Let's solve problem 71. a). The equation is $(3y - 2c)^2 - ...

EquationsSimplificationVariablesSolutionsExpansion
2025/5/25

The problem asks us to solve for $x$ in the following equation: $(2x - 3b)^2 = (x + 6b)(x - 9b)(8x -...

EquationsPolynomial EquationsVariable SubstitutionSimplification
2025/5/25

We need to solve for $x$ in the following four equations, where $m$ is a real parameter: a) $m(mx + ...

Linear EquationsQuadratic EquationsParameterSolving Equations
2025/5/25

We are asked to solve the following equations for $x$, where $a$ is a real parameter: a) $1 - 3a + 5...

Linear EquationsQuadratic EquationsSolving EquationsParameter
2025/5/25

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