options: Solve systems of equations.

Represent and solve problems involving multiplication and division.

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

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Perform arithmetic operations on polynomials.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Analyze patterns and relationships.

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Use the four operations with whole numbers to solve problems.

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

Work with addition and subtraction equations.

Write and interpret numerical expressions.

Add and subtract within 20.

Create equations that describe numbers or relationships

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

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

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

Reason about and solve one-variable equations and inequalities.

Rewrite rational expressions.

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

Gain familiarity with factors and multiples.

Multiply and divide within 100.

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

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.
problem_activity: Problem 1
In equations (a)–(d) below, the solution,
$$x$$
, to the equation depends on the constant,
$$a$$
. Assuming
$$a$$
is positive, what is the effect of increasing
$$a$$
on the solution? Does it increase, decrease, or remain unchanged?
Give a reason for your answer that can be understood without solving the equation.
a.
$$x-a=0$$
b.
$$ax=1$$
c.
$$ax=a$$
d.
$$\frac{x}{a}=1$$
Problem 2
Which of the following equations have the same solution(s)? Give reasons for your answer that do not depend on solving the equations.
a.
$${x+3=5x-4}$$
b.
$${x-3=5x+4}$$
c.
$${2x+8=5x-3}$$
d.
$${10x+6=2x-8}$$
e.
$${10x-8=2x+6}$$


correct_option_index: 8