Pre-Algebra 2-4 Solving Equations Containing Integers 2-4 Solving Equations Containing Integers...
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Pre-Algebra 2-4 Solving Equations Containing Integers 2-4 Solving Equations Containing Integers Pre-Algebra Warm Up Problem of the Day Lesson Presentation
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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 = –3
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 = –2
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
Subtract 9 from 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 newtons (N). If the net force is 5 N, 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 N.• The net force is 5 N.
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 newtons.
22 Make a Plan
5 = –23 + f
Solve33
Add 23 to both sides.
The right boat is exerting a force of 28 newtons on the rope.
5 = –23 + f+23 +23
28 = 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 N to the left. Since the total force on the tow rope was 5 N, the right tug boat was exerting a greater force in the positive direction. Thus the tug boat is moving to the right.
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.
