# A.4b - Justify Expressions

A.4b    The student will solve multistep linear and quadratic equations in two variables, including

b)  justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subsets;

Graphing calculators will be used both as a primary tool in solving problems and to verify algebraic solutions.

Bloom's Level:  Evaluate

### BIG IDEAS

• I can find how far and how fast a bus travels, the number and combinations of fruits that can be purchased, and how long it takes to drain a swimming pool.
• I will be able to write symbolic representations of the way numbers behave and will know that in order to maintain equality, an operation performed on one side must also be performed on the other side.

### UNDERSTANDING THE STANDARD

• A solution to an equation is the value or set of values that can be substituted to make the equation true.
• The solution of an equation in one variable can be found by graphing the expression on each side of the equation separately and finding the x-coordinate of the point of intersection.
• Real-world problems can be interpreted, represented, and solved using linear and quadratic equations.
• The process of solving linear and quadratic equations can be modeled in a variety of ways, using concrete, pictorial, and symbolic representations.
• Properties of real numbers and properties of equality can be used to justify equation solutions and expression simplification.
• The zeros or the x-intercepts of the quadratic function are the real root(s) or solution(s) of the quadratic equation that is formed by setting the given quadratic expression equal to zero.
• A system of linear equations with exactly one solution is characterized by the graphs of two lines whose intersection is a single point, and the coordinates of this point satisfy both equations.
• A system of two linear equations with no solution is characterized by the graphs of two lines that are parallel.
• A system of two linear equations having infinite solutions is characterized by two graphs that coincide (the graphs will appear to be the graph of one line), and the coordinates of all points on  the line satisfy both equations.
• Systems of two linear equations can be used to model two real-world conditions that must be satisfied simultaneously.
• Equations and systems of equations can be used as mathematical models for real-world situations.
• Set builder notation may be used to represent solution sets of equations.

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

A.4b1  Simplify expressions using the field properties of the real numbers and properties of equality to justify simplification.

### KEY VOCABULARY

literal equation (formula), expression, equation, properties of real numbers, properties of equality, quadratic equation, quadratic function, quadratic expression, roots, zeros, linear equation, system, substitution, elimination, ordered pair, coordinate, intersection, intercepts, solution, infinite, parallel, coincide, simultaneous

Updated: Jun 13, 2017