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

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

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 _____
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 _____
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 _____
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 _____
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 ____
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 ____
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 ____
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
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 ____
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 _____
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 ____
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 ____
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 ____
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 ____
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 ____
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 _____
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 _____
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 ______
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 _____
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 ____
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 ____
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
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? _____
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?
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 ____
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 ____
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 ____
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 ____
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 _____
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 _____
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 ____
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 _____
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 _____
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 ____
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 ____
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 ____
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 _____
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 ____
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 ____
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 ____
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 _____
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 ____
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 ____
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.
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.
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.