1. Solving Integer Equation
11-8
Solving Integer Equation
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Warm Up
Use mental math to find each solution.
x = x = 15
= x – 8 = 12
x = 6
x = 5 x 5 __
x = 20
x = 20

3. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Problem of the Day
Marie spent $15 at the fruit stand, buying peaches that cost $2 per container and strawberries that cost $3 per container. She bought the same number of containers of each fruit. How many containers each of peaches and strawberries did she buy? 3

4. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Learn to solve equations containing integers.

5. Additional Example 1A: Adding and Subtracting to Solve Equations
Course 1
11-8
Solving Integer Equations
Additional Example 1A: Adding and Subtracting to Solve Equations
Solve –8 + y = –13. Check your answer.
–8 + y = –13
–8 is added to y.
Subtracting –8 from both sides to undo the addition.
y = –5
Check
–8 + y = –13
Write the equation.
–8 + (–5) = –13 ?
Substitute –5 for y.
–13 = –13 ?
–5 is a solution. 

6. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Subtracting a number is the same as adding its opposite. To solve the equation on the previous slide using algebra tiles, you can subtract -8 tiles from both sides and then remove zero pairs.
Helpful Hint

7. Additional Example 1B: Adding and Subtracting to Solve Equations
Course 1
11-8
Solving Integer Equations
Additional Example 1B: Adding and Subtracting to Solve Equations
Solve n – 2 = –8. Check your answer.
n – 2 = –8
2 is subtracted from n.
Add 2 to both sides to undo the subtraction.
n = –6
Check
n – 2 = –8
Write the equation.
–6 – 2 = –8 ?
Substitute –6 for n.
–8 = –8 ?
–6 is a solution. 

8. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Check It Out: Example 1A
Solve –2 + y = –7. Check your answer.
–2 + y = –7
–2 is added to y.
Subtracting –2 from both sides to undo the addition is the same as adding +2.
y = –5
Check
–2 + y = –7
Write the equation.
–2 + (–5) = –7 ?
Substitute –5 for y.
-7 = -7 ?
–5 is a solution. 

9. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Check It Out: Example 1B
Solve n – 6 = –14. Check your answer.
n – 6 = –14
6 is subtracted from n.
Add 6 to both sides to undo the subtraction.
n = –8
Check
n – 6 = –14
Write the equation.
–8 – 6 = –14 ?
Substitute –8 for n.
–14= –14 ?
–8 is a solution. 

10. Additional Example 2A: Multiplying and Dividing to Solve Equations
Course 1
11-8
Solving Integer Equations
Additional Example 2A: Multiplying and Dividing to Solve Equations
Solve 4m = –20. Check your answer. 4m 4
___
-20 4
___
m is multiplied by 4. Divide both sides by 4 to undo the multiplication. =
m = –5
Check
4m = –20
Write the equation.
4(–5) = –20 ?
Substitute –5 for m.
–20 = –20 ?
–5 is a solution. 

11. Additional Example 2B: Multiplying and Dividing to Solve Equations
Course 1
11-8
Solving Integer Equations
Additional Example 2B: Multiplying and Dividing to Solve Equations
Solve = –7. Check your answer. x 3 x 3 __
3 • = 3 • (–7)
x is divided by 3. Multiply both sides by 3 to undo the division.
x = –21
Check x 3 __
= –7
Write the equation.
–21 ÷ 3 = –7 ?
Substitute –21 for x.
–7 = –7 ?
–21 is a solution. 

12. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Check It Out: Example 2A
Solve 3n = –15. Check your answer.
n is multiplied by 3. Divide both sides by 3 to undo the multiplication. 3n 3
___
-15 3
___ =
n = –5
Check
3n = –15
Write the equation.
3(–5) = –15 ?
Substitute –5 for n.
–15 = –15 ?
–5 is a solution. 

13. Solving Integer Equations
Course 1
11-8
Solving Integer Equations
Check It Out: Example 2B
Solve = –6. Check your answer. y 4 __ y 4 __
4 • = 4 • (–6)
y is divided by 4. Multiply both sides by 4 to undo the division.
y = –24
Check y 4 __
= –6
Write the equation.
–24 ÷ 4 = –6 ?
Substitute –24 for y.
–6 = –6 ?
–24 is a solution. 

14. Solving Integer Equations Insert Lesson Title Here
Course 1
11-8
Solving Integer Equations
Insert Lesson Title Here
Lesson Quiz
Solving each equation.
x = –6 2. y – 9 = –7
3. –6a = = –9
5. A submarine captain sets the following diving course: dive 300 ft, stop, and then dive another 300 ft. If this pattern is continued, how many dives will be necessary to reach a location 3,000 ft below sea level?
x = –11
y = 2 x 5 __
a = –4
x = –45 10