Go through the **Spectrum Math Grade 6 Answer Key Chapter 5 Lesson 5.5 Solving 1-Step Equations: Addition & Subtraction** and get the proper assistance needed during your homework.

## Spectrum Math Grade 6 Chapter 5 Lesson 5.5 Solving 1-Step Equations: Addition & Subtraction Answers Key

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal.

x + 12 = 20

To undo the addition of 12, subtract 12.

x + 12 – 12 = 20 – 12

x + 0 = 8

x = 8

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equation.

n – 3 = 15

To undo the subtraction of 3, add 3.

n – 3 + 3 = 15 + 3

n – 0 = 18

n = 18

**Write the operation that would undo the operation in the equation.**

Question 1.

a. x – 4 = 3 _____

Answer:

Given x – 4 = 3

To undo the subtraction of 4, add 4.

x – 4 + 4 = 3 + 4 (Adding 4 on both the sides)

x – 0 =7

x = 7

b. 8 = b + 4 _____

Answer:

Given 8 = b+ 4

To undo the addition of 4, subtract 4

8 – 4 = b + 4 – 4 (Subtracting 4 on both sides)

– 4 = b+ 0

b = -4

Question 2.

a. y + 7 = 25 _____

Answer:

Given y + 7 = 25

To undo the subtraction of 7, add 7.

y + 7 – 7 = 25 – 7 (Subtracting 7 on both sides)

y – 0 = 18

y = 18

b. 3 = a – 7 _____

Answer:

Given 3 = a – 7

To undo the subtraction of 7, add 7.

3 + 7 = a – 7 + 7 (adding 7 on both sides)

10 = a – 0

a = 10

**Solve each equation.**

Question 3.

a. a – 4 = 2 ____

Answer:

Given a – 4 = 2

To undo the subtraction of 4, add 4.

a – 4 + 4 = 2 + 4 (Adding 4 on both sides)

a – 0 = 6

a = 6

b. y + 5 = 9 ____

Answer:

Given y +5 = 9

To undo the addition of 5, subtract 5

y + 5 – 5 = 9 – 5 (Subtracting 5 on both sides)

y +0 = 4

y = 4

c. x – 3 = 14 ____

Answer:

Given x – 3 = 14

To undo the subtraction of 3, add 3

x – 3 + 3 = 14 + 3 (Adding 3 on both sides)

x – 0 = 17

x = 17

Question 4.

a. 7 = x – 4

Answer:

Given 7 = x – 4

To undo the subtraction of 4, add 4

7 + 4 = x – 4 + 4 (Adding 4 on both sides)

11 = x – 0

x = 11

b. b + 7 = 19 ____

Answer:

Given b + 7 = 19

To undo the addition of 7, subtract 7

b + 7 – 7 = 19 – 7 (Subtracting 7 on both sides)

b + 0 = 12

b = 12

c. y + 5 = 5 _____

Answer:

Given y+ 5 = 5

To undo the addition of 5, subtract 5

y + 5 – 5 = 5 – 5 (Subtracting 5 on both sides)

y + 0 = 0

y = 0

Question 5.

a. z – 7 = 5 ____

Answer:

Given z – 7 = 5

To undo the subtraction of 7, add 7

z – 7 + 7 = 5 + 7 (Adding 7 on both sides)

z – 0 = 12

z = 12

b. m – 5 = 5 ____

Answer:

Given m – 5 = 5

To undo the subtraction of 5, add 5

m – 5 + 5 = 5 + 5 (Adding 5 on both sides)

m – 0 = 10

m = 10

c. n + 1 = 1 ____

Answer:

Given n + 1 = 1

To undo the addition of 1, subtract 1

n + 1 – 1 = 1 – 1 (Subtracting 1 on both sides)

n + 0 = 0

n = 0

Question 6.

a. x + 7 = 10 ____

Answer:

Given x + 7 = 10

To undo the addition of 7, subtract 7

x + 7 – 7 = 10 – 7

x + 0 = 3

x = 3

b. x – 3 = 18 ____

Answer:

Given x – 3 = 18

To undo the subtraction of 3, add 3

x – 3 + 3 = 18 + 3 (Adding 3 on both sides)

x + 0 = 21

x = 21

c. x + 0 = 9 _____

Answer:

Given x +0 = 9

To undo the operation , add 0 on both sides

x + 0 + 0 = 9 + 0

x = 9

Question 7.

a. b + 4 = 4 _____

Answer:

Given b + 4 = 4

To undo the addition of 4, subtract 4

b + 4 – 4 = 4 – 4 (Subtracting 4 on both sides)

b + 0 = 0

b = 0

b. b – 8 = 12 ______

Answer:

Given b – 8 = 12

To undo the subtraction of 8, add 8

b – 8 + 8 = 12 + 8 (Adding 8 on both sides)

b – 0 = 12+ 8

b = 20

c. n + 8 = 12 _____

Answer:

Given n + 8 =12

To undo the addition of 8, subtract 8

n + 8 – 8 = 12 – 8 (Subtracting 8 on both sides)

n + 0 = 4

n = 4

Question 8.

a. z – 10 = 20 ____

Answer:

Given z – 10 = 20

To undo the subtraction of 10, add 10

z – 10 + 10 = 20 + 10 (Adding 10 on both sides)

z – 0 = 30

z = 30

b. z + 5 = 20 ____

Answer:

Given z + 5 =20

To undo the addition of 5, subtract 5

z + 5 – 5 = 25 – 5 (subtracting 5 on both sides)

z + 0 = 20

z = 20

c. x – 2 = 8

Answer:

Given x – 2 = 8

To undo the subtraction of 2, add 2

x – 2 + 2 = 8 + 2 (Adding 2 on both sides)

x – 0 = 10

x = 10

**Write and solve the equation for each problem below.**

Question 9.

Kelley went to the movies. She took 20 dollars with her. When she came home, she had 6 dollars. How much money did she spend? _____

Answer:

Initially, Number of dollars Kelley contain = 20

Number of dollars , when she came home = 6

Amount of money she spend = ?

Equation : x = 20 – 6

x = 14

Therefore Kelley spent 14 dollars.

Question 10.

There are 27 students in Mrs. Yuen’s homeroom. Twelve of them have home computers. How many students do not have home computers?

Answer:

Number of students in Mrs. yuen’s homeroom = 27

Number of students having home computers = 12

Number of Students do not have home computers = x = ?

Equation : x = 27 -12

= 15

Therefore 15 students do have home computers.

**Solve each equation.**

Question 1.

a. 9 + d = 16 ____

Answer:

Given 9 + d = 16

To undo the addition of 9, subtract 9

9 + d – 9 = 16 – 9 (Subtracting 8 on both sides)

d – 0 = 7

d = 7

b. y + 3 = 9 ____

Answer:

Given y + 3 = 9

To undo the addition of 3, subtract 3

y + 3 – 3= 9 – 3 (Subtracting 8 on both sides)

y – 0 = 6

y = 6

c. 12 + a = 27 ____

Answer:

Given 12 + a = 27

To undo the addition of 12, subtract 12

12 + a – 12 = 27 – 12 (Subtracting 12 on both sides)

a – 0 = 15

a = 15

Question 2.

a. 18 – b = 4 ____

Answer:

Given 18 – b = 4

To undo the subtraction of -18, add -18

18 – b – 18 = 4 – 18 (Adding -18 on both sides)

– b = – 14

b = 14

b. 23 – c = 21 _____

Answer:

Given 23 – c = 21

To undo the subtraction of -23, add -23

23 – c – 23= 21 – 23 (Adding -23 on both sides)

-c – 0 = – 2

c = 2

c. w – 11 = 11 _____

Answer:

Given w – 11 = 11

To undo the subtraction of 11, add 11

w – 11 + 11 = 11 + 11 (Adding 11 on both sides)

w – 0 = 22

w = 22

Question 3.

a. n + 8 = 41 ____

Given n + 8 = 41

To undo the addition of 8, subtract 8

n + 8 – 8 = 41 – 8 (Subtracting 8 on both sides)

n – 0 = 33

n = 33

b. 7 + m = 20 ____

Answer:

Given 7 + m = 20

To undo the addition of 7, subtract 7

7 + m – 7 = 20 – 7 (Subtracting 7 on both sides)

m – 0 = 13

m = 13

Question 3.

a. n + 8 = 41 _____

Answer:

Given n + 8 = 41

To undo the addition of 8, subtract 8

n + 8 – 8 = 41 – 8 (Subtracting 8 on both sides)

n – 0 = 41 – 8

n = 33

b. 7 + m = 20 _____

Answer:

Given 7 + m = 20

To undo the addition of 7, subtract 7

7 + m = 20 (Subtracting 7 on both sides)

7 + m – 7 = 20 – 7

m – 0 = 20 – 7

m = 13

c. 9 + s = 9 ____

Answer:

Given 9 + s = 9

To undo the addition of 9, subtract 9

9 + s – 9 = 9 – 9 (Subtracting 9 on both sides)

s – 0 = 9 – 9

s == 0

Question 4.

a. t – 18 = 5 ____

Answer:

Given t – 18 = 5

To undo the addition of 18, subtract 18

t – 18 + 18 = 5 + 18 (Subtracting 18 on both sides)

t – 0 = 5 + 18

t = 5 + 18

t = 23

b. 36 – a = 36 ____

Answer:

Given 36 – a = 36

To undo the operation , add 36 on both sides

36 – a + 36 = 36 + 36

0 – a = 36 + 36

– a = 72

a = – 72

c. 15 – b = 0 _____

Answer:

Given 15 – b = 0

To undo the operation , add -15 on both sides

15 – b – 15 = 0 – 15

0 – b = – 15

b = 15

Question 5.

a. 17 = c + 3 ____

Answer:

Given 17 = c + 3

To undo the addition of 3, subtract 3

17 – 3= c + 3 – 3 (Subtracting 3 on both sides)

17 – 3 = c – 0

14 = c

b. 29 = 5 + b ____

Answer:

Given 29 = 5 + b

To undo the addition of 5, subtract 5

29 – 5 = 5 + b – 5 (Subtracting 5 on both sides)

29 – 5 = b – 0

24 = b

c. 36 = 35 + n ____

Answer:

Given 36 = 35 + n

To undo the addition of 35, subtract 35

36 – 35 = 35 + n -35 (Subtracting 35 on both sides)

1 = n – 0

n = 1

Question 6.

a. 2 = d – 4 _____

Answer:

Given 2 = d – 4

To undo the operation add 4 on both sides

2 + 4 = d – 4 + 4

6 = d – 0

d = 6

b. 19 = 25 – a ____

Answer:

Given 2 = d – 4

To undo the operation add -19 on both sides

19 – 19 = 25 – a

0 = 25 – a

a = 25

c. 12 = t – 12 ____

Answer:

Given 12 = t – 12

To undo the operation add -12 on both sides

12 – 12 = t – 12 – 12

0 = t – 14

t = 14

**Write an equation for each problem. Then, solve the equation.**

Question 7.

Ruben read 37 pages in his history book over the weekend. He read 21 pages on Saturday. How many pages did he read on Sunday?

_____ He read ____ pages on Sunday.

Answer:

Number of pages read over a weekend = 37

Number f pages read on Saturday = 21

Number of pages read on Sunday = p = ?

Equation : 21 + p = 37

p = 37 -21

p = 16

Therefor, Ruben read 16 pages on Sunday.

Question 8.

The Garcias ate 9 pieces of toast for breakfast. If there are 33 slices of bread left, how many slices were in the loaf of bread?

_____ There were ____ slices in the loaf of bread.

Answer:

Let the total number of Bread slices = L

Number of pieces of toast for breakfast ate by Garcias = 9

Number of bread slices left = 33

Equation : L – 9 =33

L = 33 + 9

L = 42

Therefore, 42 slices are there in the Loaf of bread.

Question 9.

In a 25-kilometer triathlon, competitors swim 2 kilometers, run 5 kilometers, and bike the rest. How far do they bike?

____ They bike ____ kilometers.

Answer:

Total number of kilometers in a triathlon = 25

number of kilometers Swim by competitors = 2

number of kilometers run by competitors = 5

number of kilometers biked by competitors = b = ?

Equation : 2 + 5 + b = 25

7 + b = 25

b = 25 – 7

b = 18 kilo meters.