Pre-Algebra

2-4 Solving Equations Containing Integers

Today’s Learning Goal Assignment

Learn to solve equations with

integers.

Pre-Algebra

2-4 Solving Equations Containing Integers

Pre-Algebra: 2-4 HW

Page 734(Yes, page 734)

#1-53 ODD

Pre-Algebra

2-4 Solving Equations Containing Integers2-4 Solving Equations Containing Integers

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

2-4 Solving Equations Containing Integers

Warm UpAdd, subtract, multiply, or divide.

Pre-Algebra

2-4 Solving Equations Containing Integers

41 4

–4236

–8

1. 24 + 17 2. 23 – 19

3. 12 · 3 4. 6(–7)

5. 6. –250 + (–85)–64 8

–335

Pre-Algebra

2-4 Solving Equations Containing Integers

Problem of the Day

What are the numerical values of the ,

the , and the ?

= 6, = 4, = 5

+ + = 15 + – = 3 + – = 5 + – = 7

Pre-Algebra

2-4 Solving Equations Containing Integers

Learn to solve equations with integers.

Pre-Algebra

2-4 Solving Equations Containing Integers

When you are solving equations with integers, your goal is the same as with whole numbers:isolate the variable on one side of the equation.

0

+ –

–

–

+

+

3 + (–3) = 0

a + (–a) = 0

Recall that the sum of a number and its opposite is 0. When you add the opposite to get 0, you can isolate the variable.

Pre-Algebra

2-4 Solving Equations Containing Integers

x = – 3

x – 3 = – 6

Add 3 to both sides.x – 3 + 3 = – 6 + 3

–5 + r = 9

r = 14Add 5 to both sides.–5 + 5 + r = 9 + 5

x – 3 + 3 = – 3Commutative Property

0

x – 3 = – 6

–5 + r = 9

Additional Example 1A & 1B: Adding and Subtracting to Solve Equations

Solve.

A.

B.

Pre-Algebra

2-4 Solving Equations Containing Integers

–6 + 8 = n

2 = n

The variable is already isolated.

Add integers.

–6 + 8 = n

z + 6 = –3

z = –9

Add –6 to each side.z + 6 = –3–6 –6

Solve.

C.

D.

Additional Example 1C & 1D: Adding and Subtracting to Solve Equations Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

p = –2

p – 7 = – 9

Add 7 to both sides.p – 7 + 7 = – 9 + 7

–2 + g = 5

g = 7Add 2 to both sides.–2 + 2 + g = 5 + 2

p – 7 = – 9

–2 + g = 5

Solve.

Try This: Example 1A & 1B

p – 7 + 7 = – 2Commutative Property

0

A.

B.

Pre-Algebra

2-4 Solving Equations Containing Integers

–1 + 7 = r

6 = r

The variable is already isolated.

Add integers.

–1 + 7 = r

a + 9 = –9

a = –18

Add –9 to each side.

Try This: Example 1C & 1D

a + 9 = –9–9 –9

Solve.

C.

D.

Pre-Algebra

2-4 Solving Equations Containing Integers

x = –7

–5x = 35

Divide both sides by –5.–5x = 35–5 –5

Additional Example 2A: Multiplying and Dividing to Solve Equations Continued

Solve.

A.

Pre-Algebra

2-4 Solving Equations Containing Integers

Multiply both sides by –4.

z = –20

= 5z –4

–4 = –4 5z –4

Additional Example 2B: Multiplying and Dividing to Solve Equations Continued

Solve.

B.

Pre-Algebra

2-4 Solving Equations Containing Integers

x = –6

–7x = 42

Divide both sides by –7.

Try This: Example 2A

–7x = 42–7 –7

Solve.

A.

Pre-Algebra

2-4 Solving Equations Containing Integers

Multiply both sides by –3.

z = –27

= 9z –3

–3 = –3 9z –3

Solve.

B.

Try This: Example 2

Pre-Algebra

2-4 Solving Equations Containing Integers

Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature was –8°F. What was the temperature at midnight?

Additional Example 3: Problem Solving Application

Pre-Algebra

2-4 Solving Equations Containing Integers

temperature at midnight

morning temperature

degrees that temperature

dropped– =

The answer is the temperature at midnight.

List the important information:• The temperature dropped 26 degrees since midnight. In the morning it was –8°F.

11 Understand the Problem

Show the relationship or the information:

Additional Example 3 Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

Write an equation and solve it. Let t represent the temperature at midnight and use the equation model. t – 26 = –8

t – 26 = –8

Add 26 to both sides.t = 18

The temperature at midnight was 18° F.

22 Make a Plan

Solve33

+ 26 + 26

Additional Example 3 Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

Look Back44

The temperature at midnight was positive. Its value is less than the absolute value of the drop in temperature. This makes sense, since the morning temperature was negative.

Additional Example 3 Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

Tim has two tug boats in a pulling contest. The boat on the left was pulling with a force of 23 tons. If the net force is 50 tons, what force is the boat on the right exerting on the rope?

Try This: Example 3

Pre-Algebra

2-4 Solving Equations Containing Integers

The answer is the force that the right tug boat is exerting.

List the important information:• The boat on the left pulls with a force of 23 tons.• The net force is 50 tons.

Show the relationship of the information:

11 Understand the Problem

Try This: Example 3 Continued

net force

left boat’s force

= right boat’s force

+

Pre-Algebra

2-4 Solving Equations Containing Integers

–

Write an equation and solve it. Let f represent the force in tons.

22 Make a Plan

50 = 23 + f

Solve33

Add –23 to both sides.

The right boat is exerting a force of 27 tons.

50 = 23 + f–23 –23

27 = f

Try This: Example 3 Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

Look Back44

The left tug boat was pulling at a force of 23 tons to the left. The total force on the tow rope was 50 tons. Since 23 tons is less than half the force, the tug boat on the right was advancing forward in a positive direction while the left tug boat was moving backward in a negative direction.

Try This: Example 3 Continued

Pre-Algebra

2-4 Solving Equations Containing Integers

Lesson Quiz: Part 1

Solve.

1. t + 9 = –8

2. –15 = 3b

4. z – 16 = 30

x–4

3. = –7

t = –17

b = –5

x = 28

z = 46

Pre-Algebra

2-4 Solving Equations Containing Integers

A roller coaster descends down a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster riders to reach the bottom?

Lesson Quiz: Part 2

5 seconds

5.