Algebra

Problems related to equations, functions, polynomials, etc.

Problems in this category

We are asked to solve three systems of equations and inequalities. Each system consists of an inequa...

EquationsInequalitiesSystems of EquationsQuadratic EquationsCubic EquationsSolving Equations

The problem asks us to solve three equations for $x$, $y$, and $z$ respectively. a) $\frac{1.3 - 3x}...

Linear EquationsSolving EquationsAlgebraic Manipulation

The problem asks to find the values of $m$ for which the function $f(x) = (3m-6)x + 2m+3$ is an incr...

Linear FunctionsInequalitiesIncreasing Function

The problem is to simplify the expression $M = (sin\theta - cos\theta)^2 + 2sin^2\theta + cot\theta$...

TrigonometryTrigonometric IdentitiesSimplificationDouble Angle Formulas

We need to analyze the given functions and sketch their graphs. I will address part (a) of the prob...

Piecewise FunctionsAbsolute ValueFunction AnalysisGraphing

Solve the equation $|x| + 2(x - 3) = 6$ for $x$.

Absolute ValueLinear EquationsEquation SolvingCase Analysis

The problem is to solve the following absolute value equations: a) $|x-2| + |x+5| = 7$ b) $|x+4| - |...

Absolute Value EquationsSolving EquationsInequalitiesCase Analysis

We are given the following system of equations: $ax + by = c^2$ $\frac{a+x}{b} = \frac{b+y}{a}$ $x -...

Systems of EquationsLinear EquationsVariable SubstitutionEquation Solving

The problem presents three systems of linear equations. We will solve the third system of equations ...

Linear EquationsSystems of EquationsElimination MethodSolving Equations

We are given a system of six linear equations with six variables, $x_1, x_2, x_3, x_4, x_5, x_6$. Th...

Linear EquationsSystems of EquationsSolving Equations

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