options: Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

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

Work with addition and subtraction equations.

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Analyze patterns and relationships.

Create equations that describe numbers or relationships

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

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve equations and inequalities graphically.

Interpret the structure of expressions.

Write expressions in equivalent forms to solve problems.

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

Multiply and divide within 100.

Solve equations and inequalities in one variable.

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

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Reason about and solve one-variable equations and inequalities.

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

Represent and solve problems involving multiplication and division.

Add and subtract within 20.

Use polynomial identities to solve problems.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

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

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

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

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.
problem_activity: Problem 1
Consider the equation
$${ {|x|=5}}$$
.
This can be thought of as a system of equations, where
$${f(x)=\left | x \right |}$$
$${{g(x)}=5}$$
and
$${f(x)={g(x)}}$$
Graph
$${f(x) }$$
and
$${g(x)}$$
in the coordinate plane. Based on the graph, what are the solutions to
$${|x|=5}$$
?
Problem 2
For each absolute value equation below, answer the questions that follow.
$${|x|=-4}$$
$${ |x|=0}$$
$${ |x|=4}$$
How many solutions are there for
$$x$$
in each equation?
Thinking of each equation as two equal functions (similar to Anchor Problem #1), what does each one look like in the coordinate plane? Where do you see the solution(s)?
Problem 3
Solve each absolute value equation algebraically and verify the solution graphically.
$${|x+2|=8}$$
$${|x|+2=8}$$
$${|x+2|+1=0}$$


correct_option_index: 11

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