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Algebra: Reasoning with Equations and Inequalities

1131 preguntas48 habilidades

Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
 Pronto habrá nuevas habilidades para este estándar.


156 preguntas6 habilidades
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.


76 preguntas3 habilidades
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.


97 preguntas3 habilidades
Use the method of completing the square to transform any quadratic equation in x into an equation of the form (xp)2 = q that has the same solutions. Derive the quadratic formula from this form.


24 preguntas1 habilidad
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
 Pronto habrá nuevas habilidades para este estándar.


70 preguntas3 habilidades
Represent a system of linear equations as a single matrix equation in a vector variable.


56 preguntas3 habilidades
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).


114 preguntas6 habilidades
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.


46 preguntas3 habilidades
Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.