Mathematics I Reasoning With Equations and Inequalities

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Reasoning With Equations and Inequalities

Resources

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.
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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
context.
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.
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6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two
variables.
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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).
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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.
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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.
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