Unit 2 – Week 4 Reasoning with Linear Equations and Inequalities Lesson 1

Learning Objective Students will understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false. Students find values to assign to the variables in equations that make the equations true statements.

Standards MGSE9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear (integer inputs only). MGSE9-12.A.REI.1 Using algebraic properties and the properties of real numbers, justify the steps of a simple, one-solution equation. Students should justify their own steps, or if given two or more steps of an equation, explain the progression from one step to the next using properties.

Essential Questions How do equations help us solve problems? How do equations help us sort information? What is the purpose of using variables? When we solve an equation what does it tell us?

Vocabulary Words Equation – A statement of equality between two expressions Variable Properties of Equality An equation is said to be true if both numerical expressions are equivalent (that is both evaluate to the same number).

Read, Write, Draw, Solve Write a word problem that the equation below could model. 2x = 12

Activator Discuss with your partner if you believe the equations listed below are TRUE or FALSE o = o ½ + 3/2 = o = (4 + 5) 2 o 6n + 12 = 6(n + 2)

When algebraic equations contain a symbol (variable) whose value has not yet been determined we have to analyze it to determine if 1.The equation is true for all the possible values of the variable(s), or 2.The equation is true for a certain set of possible value(s) of the variable(s), or 3.The equation is never true for any of the possible values of the variable(s)

Decide if each algebraic equation below is true for all, some or no values of x. Be specific in your explanations. 1.2(x+3) = 2x x + 5 = 11 3.x 2 = -1

What would we name the variable to make the equation below true? A. N 2 = 4 B.7 + x = 12 C.4(x – 3) + 3 = 23 D.X + 67 = x + 68 E.D 3 = -125 F.2a = a + a

Suppose we are told that b has a value of 4. Can we determine whether the equation below is true or false? Justify your answer. = + 1

Is there a value that we can give b to make the equation true Justify your answer. = + 1

Fill in each box so that the given value of the variable will make each equation true? A.4b – = 100 if b = 25 B.4y – = 0 if y = 24 C.r + = r if r is any real number D.t( ) = r if r is all any real number

In the following equations, let x = - 3 and y=2/3. Determine whether the following equations are true, false, or neither true nor false. A. xy=-2B. x+3y=-1 C. x+y=4 D. 9y=-2x E. yx=-2 F. -2xy=-1

Which equations below are never true for any of the possible value(s) of the variable(s) where the value(s) are real numbers? Explain your reasoning. A. X 2 = -1 B. = 5

Summarizer Generate the following: A.An equation that is always true B.An equation that is true when x=0 C.An equation that is never true D.An equation that is true when t=1 or t=-1