options: Understand the connections between proportional relationships, lines, and linear equations.

Interpret the structure of expressions.

Work with radicals and integer exponents.

Use polynomial identities to solve problems.

Work with equal groups of objects to gain foundations for multiplication.

Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Write and interpret numerical expressions.

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

Understand and apply properties of operations and the relationship between addition and subtraction.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Create equations that describe numbers or relationships

Represent and analyze quantitative relationships between dependent and independent variables.

Understand properties of multiplication and the relationship between multiplication and division.

Solve equations and inequalities in one variable.

Reason about and solve one-variable equations and inequalities.

Work with addition and subtraction equations.

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Multiply and divide within 100.

Use the four operations with whole numbers to solve problems.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

Generate and analyze patterns.
problem_activity: Given below are the graphs of two lines,
$${y = 0.5x + 5}$$
and
$${y = -1.25x + 8}$$
, and several regions and points are shown. Note that C is the region that appears completely white in the graph.
[IMG]
For each region and point, write a system of equations or inequalities that has the region or point as its solution set.
Verify that a point that lies in region A satisfies the system of inequalities that you wrote for region A.
Without choosing any specific numbers, explain how you know that all the points in quadrant 3 must satisfy the inequalities for region A.


correct_option_index: 6

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