The document provides instructions on solving integer equations using inverse operations. It lists the rules for adding, subtracting, multiplying and dividing integers. It then provides 21 practice problems to solve integer equations, with the solutions shown. The goal is to use inverse operations to isolate the variable term and apply the integer rules to determine its value.

1. Name __________________________________ Date ______________________
Mrs. Labuski / Mrs. Rooney Period ________ Lesson 9-8 Integer Equations
Remember to use inverse operations to get the integer alone.
Don’t forget your integer rules:
When adding:
If the integers are the same, add the digits, keep the sign
If the integers are different, take the difference of the digits, take sign of the larger digit.
When subtracting:
Keep the first digit, Change subtraction to addition, Change sign of second number
If the integers are the same, add the digits, keep the sign
If the integers are different, take the difference of the digits, take sign of the larger digit.
When multiplying and dividing
Multiply or divide as usual
If the integers are the same, the product / quotient is positive
If the integers are different, the product / quotient is negative
1. x - 4 = -10 2. -2x = 8
3. -3 + x = 12 4. x ÷ 6 = -9
5. -7 + x = -15 6. 35 = -5x
Solve each equation.
7. -45 ÷ x = -5 8. x - 9 = -1 9. 36 ÷ x = -6
10. x - 10 ÷ -12 11. -8x = 56 12. x ÷ 7 = -9

2. 13. 3x = -36 14. 15 + x = 21 15. -4x = 64
16. x ÷ (-3) = -5 17. x ÷ -12 = -5 18. x - 13 = -9
19. -7 + x = 4 20. -9x = 54 21. 49 ÷ x = -7
Name __________________________________ Date ______________________
Mrs. Labuski / Mrs. Rooney Period ________ Lesson 9-8 Integer Equations
Remember to use inverse operations to get the integer alone.
Don’t forget your integer rules:
When adding:
If the integers are the same, add the digits, keep the sign
If the integers are different, take the difference of the digits, take sign of the larger digit.
When subtracting:
Keep the first digit, Change subtraction to addition, Change sign of second number
If the integers are the same, add the digits, keep the sign
If the integers are different, take the difference of the digits, take sign of the larger digit.
When multiplying and dividing
Multiply or divide as usual
If the integers are the same, the product / quotient is positive
If the integers are different, the product / quotient is negative
1. x - 4 = -10 2. -2x = 8
+4 +4 ÷(-2) ÷(-2)
x = -6 x = -4
3. -3 + x = 12 4. x ÷ 6 = -9
+3 +3 •6 •6
x = 15 x = -54
5. -7 + x = -15 6. 35 = -5x
+7 +7 ÷(-5) ÷(-5)
x = -8 -7 = x

3. Solve each equation.
For division, the inverse operation only works when the first digit (dividend) is x
For example: -45 ÷ x = -5 inverse operation will not work
x ÷ 7 = -9 inverse operation will work
7. -45 ÷ x = -5 8. x - 9 = -1 9. 36 ÷ x = -6
x = 9 +9 +9 x = -6
x = -8
10. x - 10 = -12 11. -8x = 56 12. x ÷ 7 = -9
+10 +10 ÷(-8) ÷(-8) •7 •7
x = -2 x = -7 x = -63
13. 3x = -36 14. 15 + x = 21 15. -4x = 64
÷3 ÷3 -15 -15 ÷(-4) ÷(-4)
x = -12 x= 6 x = -16
16. x ÷ (-3) = -5 17. x ÷ -12 = -5 18. x - 13 = -9
• (-3) • (-3) • (-12) • (-12) +13 +13
x = 15 x = 60 x=4
19. -7 + x = 4 20. -9x = 54 21. 49 ÷ x = -7
+(-7) +(-7) ÷(-9) ÷(-9) x = -7
x = -3 x = -6