Mathematics I Reasoning With Equations and Inequalities


Reasoning With Equations and Inequalities


Understand solving equations as a process of reasoning and explain the reasoning.
[Master linear; learn as general principle.]
1. 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.
Solve equations and inequalities in one variable.
3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [Linear inequalities; literal equations that are linear in the variables being solved for; exponential of a form, such as 2x-1/16.] tools-icon
3.1 Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in
Solve systems of equations. [Linear-linear and linear-quadratic]
5. 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.
6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two
Represent and solve equations and inequalities graphically. [Linear and exponential; learn as general principle.]
10. 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).
11. 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.
12. 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.