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

Use polynomial identities to solve problems.

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

Perform arithmetic operations on polynomials.

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

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

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

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

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

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

Represent and analyze quantitative relationships between dependent and independent variables.

Write and interpret numerical expressions.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

Analyze patterns and relationships.

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.

Represent and solve problems involving multiplication and division.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

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

Solve equations and inequalities in one variable.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

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

Gain familiarity with factors and multiples.

Create equations that describe numbers or relationships
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: 13

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