SWBAT Simplify One Variable Equations and Identify If an Equation Has Infinite, One Or

8.EE.7a

Standard: a) Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers).

SWBAT simplify one variable equations and identify if an equation has infinite, one or no solutions.

Develop:

Activity #1 The Sign of Solutions

Describe whether these equations have a positive solution, a negative solution, a zero solution, or no solution.

1. 3x =5 2. 5z +7=3 3. 7−5w =3 4. 4a =9a 5. y =y +1

Adapted from Algebra: Form and Function, McCallum, Wiley, 2010. Posted on illustrativemathematics.org Activity #2 Grouping

Solve and compare these six problems by putting them into groups. Justify your reasoning for the groups.

1. 2x +6 = 12

2. 4x – 3 = 4x -3

3. 2x=4

4. 2x – 6 = 2x +7

5. 2(x+3) = 2x + 6

6. x + 2 = x +1 s 3(4s + 8) 2 (12 + 6s) Solidify: Table Trouble:

Evaluate each expression for different values of s. Then tell what you know about the expressions.

Evaluate each expression for different values of n. Then tell what you know about the expressions.

n 3(4n + 8) 2 (10 + 6n) 2. Evaluate each expression for different values of x. Then tell what you know about the expressions.

3. x 2x + 6 4x - 8

Practice:

Sort the following equations into groups with either no solution, one solution or infinitely many solutions. x = 2/5 3h = 12 4(n – 2) -1 = 5n – n + 9 r = 5r -3r –r 1/2 = 5/10 2j + 7 =2j +7 2/10 = 0.02 4 = 9

Explain how to identify whether an equation has one solution, no solution or infinitely many solutions. Assessment:

Write an equation with one solution. Write an equation with no solution. Write an equation with infinitely many solutions.