inverse operations
What is the inverse operation of addition?
Subtraction
x + 12 = 0
x = -12
6x – 13 = 11
x = 4
Twice a number increased by 9 is equal to 25.
2x + 9 = 25
Express the situation in an equation: A parking garage charges a $5 entrance fee plus $2 per hour. Carla paid $19 total.
2x + 5 = 19
What is the inverse operation of subtraction?
Addition
4 = -8 + x
x = 12
3x + 5 = 14
x = 3
Three times a number decreased by 12 is equal to 6.
3x − 12 = 6
Express the situation in an equation: A delivery service charges a $7 base fee plus $0.80 per kilometer. The total cost was $19.
0.8x + 7 = 19
What is the inverse operation of multiplication?
Division
-16 = x+2
x = -18
29 = 4 + 5x
x = 5
Eight more than three times a number is equal to 32.
3x + 8 = 32
Express the situation in an equation: The perimeter of a rectangle is 64 cm. The length is 4 cm more than three times the width.
8x + 8 = 64
What is the inverse operation of division?
Multiplication
5x = -80
x = -16
-8 = 2x + 16
x = -12
Six less than four times a number is equal to 10.
4x − 6 = 10
Express the situation in an equation: A rope is cut into two pieces. One piece is 5 meters longer than the other. The total length is 29 meters.
2x + 5 = 29
What would be the inverse of dividing by -9?
Multiplying by -9
3 = -2 – x
x = -5
4 = -7x + 32
x = 4
Three less than twice a number is equal to negative 8.
2x − 3 = −8
Express the situation in an equation: A runner completed a total of 32 km over 7 training days. On the first day, she ran 2 km. On the other days, she ran the same distance each day.
6x + 2 = 32