A.REI

Reasoning with Equations and Inequalities

A.REI.1(all) 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.A.REI.10(9/10) 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.A.REI.2(all) Apply and extend previous understanding to solve equations, inequalities, and compound inequalities in one variable, including literal equations and inequalities.A.REI.3Solve equations in one variable and give examples showing how extraneous solutions may arise.A.REI.3a(9/10/11) Solve rational, absolute value and square root equations. (9/10) Limited to simple equations such as, 2√x−3 + 8 = 16, x+3/2x-1 = 5, x ≠ 1/2.A.REI.3b(+) Solve exponential and logarithmic equations.A.REI.4(11) Solve radical and rational exponent equations and inequalities in one variable, and give examples showing how extraneous solutions may arise.A.REI.5Solve quadratic equations and inequalities.A.REI.5a(9/10) Solve quadratic equations by inspection (e.g. for x^2 = 49), taking square roots, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives no real solutions.A.REI.5b(11) Solve quadratic equations with complex solutions written in the form a +/- bi for real numbers a and b.A.REI.5c(11) Use the method of completing the square to transform and solve any quadratic equation in x into an equation of the form (x - p)^2 that has the same solutions.A.REI.5d(+) Solve quadratic inequalities and identify the domain.A.REI.6(9/10) Analyze and solve pairs of simultaneous linear equations.A.REI.6a(9/10) Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.A.REI.6b(9/10) Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.A.REI.6c(9/10) Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.A.REI.7(+) Represent a system of linear equations as a single matrix equation and solve (incorporating technology) for matrices of dimension 33 or greater.A.REI.8(all) Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).A.REI.9(9/10/11) Solve an equation f(x) = g(x) by graphing y = f(x) and y = g(x) and finding the x-value of the intersection point. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. For (9/10) focus on linear, quadratic, and absolute value.
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