Lesson 3

Lesson 3Slide 1

Unknown LocationsEE.10 Evaluate an expression for specific values of the variable(s).

EE.11 Understand that a solution to an equation is a value or set of values of the variable(s) for which the equation is a true statement.

EE.12 Determine if a specific value or set of values is a solution to an equation.

EE.16 Solve one-step and multi-step linear equations in one variable.

EE.18 Find solutions to equations with two variables.

EE.19 Understand that a two-variable linear equation (such as x + y = 6) can be used as a formula for determining another number when one number is given.

Chapter 1

Lesson 3

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Lesson 3Slide 2

Objectives

• Evaluate expressions for specific values of a variable.

• Solve one step equations in one variable.

• Find solutions to equations with two variables.

Lesson 3Slide 3

Remember from Before

• What is an equation?

• What is a variable?

Lesson 3Slide 4

Get Your Brain in GearQuickly find the value of each expression when h = 7.

Quickly find the value of each expression when w = 9.

b. h + h

d. 8 + h

c. 5 + h

a. 3 + h

a. w + w

b. 7 + w

c. 3 + w

d. 8 + w

10

12 15

12

14

1618

17

Lesson 3Slide 5

We use letters to show unknown values. What are these letters called?

Lesson 3Slide 6

This means that b has an unknown location.

Lesson 3Slide 7

1. Based on the way the following points are marked, which have known locations and which have unknown locations?

Check for Understanding

0 is always known. By the way the points are marked, points j and m have known locations, while points k and d have unknown locations.

Lesson 3Slide 8

1 + b is an expression for an unknown location.

Lesson 3Slide 9

If 1 + b = 4, as shown below, what is the value of b?

If b = 2, as shown below, what is the value of 1 + b?

?

Lesson 3Slide 10

2. What is the value of 1 + b when b is 1? What about when b is 4?


When b = 1, 1 + b =

When b = 4, 1 + b = 5

2

Lesson 3Slide 11

Let’s list different possible values of b and 1 + b in a table:

Lesson 3Slide 12

What would happen if b is zero?

1 + b would have a value of 1.

Lesson 3Slide 13

Here is a table showing some of the values of t and t + 3.

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What is the value of t?

We know that the value of t + 3 is 5.

So it is easy to see that t is equal to 2.

Lesson 3Slide 15

Let’s add t = 2 and t + 3 = 5 to the table of values.

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3. Fill in the missing values in the table below for k and k + 4:


5

4

6

Lesson 3Slide 17

In symbols, the equation is:

2 + c = d

Lesson 3Slide 18

These values form a solution to the equation because they make 2 + c equal to d.

Lesson 3Slide 19

These values form a solution to the equation because they make 2 + c equal to d.

Lesson 3Slide 20

What about values c = 2 and d = 5?

The two expressions are not equal, so c = 2, d = 5 is NOT a solution to the equation 2 + c = d.

Lesson 3Slide 21

4. Which of the following are solutions to the equation 2 + c = d ?


This is a solution because 2 + 2 = 4.

This is not a solution because 2 + 0 does not equal 1.

This is a solution because 2 + 0 = 2.

Lesson 3Slide 22

When w = 2, what is the value of z that forms a solution?

When w = 2, we can replace w with 1 + 1, and we can always replace 3 with 1 + 1 + 1.So, w + 3 is replaced with 1 + 1 + 1 + 1 + 1.Now we can see that when w = 2, then z = 4 is a solution to this equation.

Lesson 3Slide 23

5. Fill in the missing values in the following table of solutions:


w + 3 = 1 + z 6

5

9

Lesson 3Slide 24

Multiple Choice Practice

1. When you find a solution to an equation, which of the following happens?

Lesson 3Slide 25

Find the Errors

The first mistake is in the second row, because 1 + 3 does not equal 3. Either w must change to 0 or n must change to 4. The second mistake is in the fourth row, since 8 + 3 does not equal 12. Either w must change to 9 or n must change to 11.

Technology

Lesson 3