Solve real-world and mathematical problems by writing and solving equations of the form π₯ Β± π = π and ππ₯ = π for cases in which π, π and π₯ are all nonnegative rational numbers.
Algebra and Functions
Expressions & Equations: Reason about and solve one-variable equations and inequalities.
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Solve word problems leading to equations of the form ππ₯ Β± π = π and π(π₯ Β± π) = π, where π, π, and π are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
Expressions & Equations: Understand the connections between proportional relationships, lines, and linear equations.
Use similar triangles to explain why the slope π is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation π¦ = ππ₯ for a line through the origin and the equation π¦ = ππ₯ + π for a line intercepting the vertical axis at π.
Solve linear equations with rational number coefficients, including equations with variables on both sides and whose solutions require expanding expressions using the distributive property and collecting like terms.
Record information about constant rates of change in graphs and equations.
Solve real-world and mathematical problems by writing and solving equations of the form πΉ + π± = π² and π±πΉ = π² for cases in which π±, π² and πΉ are all nonnegative rational numbers.
Solve real-world and mathematical problems by writing and solving equations of the form πΉ + π± = π² and π±πΉ = π² for cases in which π±, π² and πΉ are all nonnegative rational numbers.
Solve real-world and mathematical problems by writing and solving equations of the form πΉ + π± = π² and π±πΉ = π² for cases in which π±, π² and πΉ are all non-negative rational numbers.
Solve real-world and mathematical problems by writing and solving equations of the form π₯ + π = π and ππ₯ = π for cases in which π, π and π₯ are all nonnegative rational numbers.
Solve real-world and mathematical problems by writing and solving equations of the form πΉ + π± = π² and π±πΉ = π² for cases in which π±, π² and πΉ are all nonnegative rational numbers.
