options: Work with addition and subtraction equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

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

Reason about and solve one-variable equations and inequalities.

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

Add and subtract within 20.

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

Create equations that describe numbers or relationships

Generate and analyze patterns.

Solve equations and inequalities in one variable.

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

Multiply and divide within 100.

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

Write and interpret numerical expressions.

Analyze patterns and relationships.

Represent and solve problems involving addition and subtraction.

Use polynomial identities to solve problems.

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

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

Represent and solve problems involving multiplication and division.

Interpret the structure of expressions.

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

Perform arithmetic operations on polynomials.

Use properties of operations to generate equivalent expressions.

Use the four operations with whole numbers to solve problems.

Write expressions in equivalent forms to solve problems.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve equations and inequalities graphically.

Rewrite rational 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: 22

32