Unit 2 – Week 4Reasoning with Linear Equations and Inequalities

Lesson 2

Students understand that an equation with variables is often viewed as a question asking for the set of values one

can assign to the variables of the equation to make the equation a true statement. They see the equation as a

“filter” that sifts through all numbers in the domain of the variables, sorting those numbers into two disjoint sets: the solution set and the set of numbers for which the

equation is false.

Standards

• A.REI.1 – Using algebraic properties and the properties of real numbers, justify the steps of a simple one-solution equation.

• A.REI.3 – Solve linear equations in one variable including equations with coefficients represented by letters.

Essential Questions

• What does it mean to solve an equation?• Do all equations have the same number of solutions

meaning 1, 0 or infinite?• Why would an equation have only 1 solution? 0

solutions? Infinite solutions?• What does it mean for two expressions to be

algebraically equivalent?• When the left side of an equation is algebraically

equivalent to the right side of the equation, what will the solution set be?

Vocabulary Words

• Solution Set: A set of solutions to an equation• Set Notation: A way to list a solution set using

brackets• Empty Set: No possible solutions• Solve: To find the solution set for an equation

Read, Write, Draw, Solve

• Complete “Cookie Sale 2” Task• Discuss

Activator

Describe the solution set for x2 = 25

A. In WordsB. Solutions ListedC. On a number line

Activator Discussion

Describe the solution set for x2 = 25

A. This equation is true when x = 5 or x = -5B. {-5, 5}C.

Solve for a: a2 = -25

Present the solution set in the form of words, set notation and graphically.

7 + x = 12

Present the solution set in the form of words, set notation and graphically.

Present the solution set in the form of words, set notation and graphically.

Would the solution set change for the equation

if we ask “what are the value(s) of x over the set of all non-zero real numbers”

What is the solution set for all real numbers in the equation below? Use words, set notation and a graph to justify your answer.

x(3 + x) = 3x + x2

Recap

• Discuss with a partner what the solution set of each equation below is. Record your answers in words, set notation and graphically.

A. x2 = 49B. x + 8 = 18C. x(x + 5) = x2 + 5x

Summarizer

Complete the Exit Ticket