Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are given a sequence ${a_n}$ such that $a_1 = 1$ and $a_{n+1} = 3a_n + 2$. We need to find the va...

Sequences and SeriesRecursive Sequences

Solve the equation $3^{2x} - 30 = 3^x$.

Exponential EquationsQuadratic EquationsLogarithmsChange of Base

The problem is to solve the system of two equations: $b = -a$ $-12 = -6a$ for the variables $a$ and ...

Linear EquationsSystem of EquationsSolving Equations

We are given the inequality $x^2 - 10x + c > 0$. We need to find the range of values for the constan...

Quadratic InequalitiesDiscriminantCompleting the SquareInequalities

The problem is to solve the equation $5|3-x| - 51 = 4$ for $x$. This involves isolating the absolute...

Absolute Value EquationsSolving Equations

The problem is to solve the linear equation $4(x - 2) + 5x = 9x + 8$ for $x$.

Linear EquationsSolving Equations

The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$. We need to determine th...

SequencesGeometric SequenceSeriesFormulaCommon Ratio

We are given a sequence $(U_n)$ defined by the initial term $U_0 = 1$ and the recursive relation $3U...

SequencesSeriesGeometric SequenceConvergence

Given the matrix $A = \begin{pmatrix} 1 & 0 & 1 \\ 2 & 1 & 0 \\ -1 & 2 & 3 \end{pmatrix}$, we need t...

Linear AlgebraMatricesDeterminantsInverse MatrixSystem of Equations

We are given a system of two linear equations with two variables, $x$ and $y$. We need to solve for ...

Linear EquationsSystems of EquationsElimination MethodSolving Equations

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