## Math 6 Chapter 2 Lesson 9: Transition rules

## 1. Summary of theory Tóm

### 1.1. The property of equality

When transforming equations, we usually apply the following properties:

- If a = b then a + c = b + c
- If a + c = b + c then a = b
- If a = b then b = a

### 1.2. Transition rule

When moving a term from one side of an equality to another, we must change the sign of that term: the “+” sign changes to “-” and the “-” sign changes to the “+” sign.

**Comment:**

– We already know a – b = a + (-b), so (a – b) + b = a + [(-b) + b] = a + 0 = a.

– Conversely, if x + b = a, then after switching sides, we get x = a – b

– So the difference a – b is the number that when adding that number to b will get a, or we can say subtraction is the inverse operation of addition.

## 2. Illustrated exercise

**Question 1: **Find an integer x, know: x – 2 = -3

**Solution guide:**

x – 2 = -3

x – 2 + 2 = -3 +2

x = -3 +2

x = -1

**Verse 2: **Find an integer x, knowing:

a. x – 2 = – 6

b. x – (-4) = 1

**Solution guide:**

a. x – 2 = – 6

x = – 6 + 2

x = -4

b. x – (-4) = 1

x + 4 = 1

x = 1 – 4

x = -3

**Question 3: **Find an integer a, knowing:

a. |a| = 7

b. |a + 6| = 0

**Solution guide:**

a. |a| = 7 so a = 7 or a = -7

b. |a + 6| = 0 so a + 6 = 0 or a = 6

## 3. Practice

### 3.1. Essay exercises

**Question 1: **Find \(a \in \mathbb{Z}\). Find an integer x, knowing:

a. a + x = 7

b. a – x = 25

**Verse 2: **It has been proven that:

The distance between two points a, b on the number line \((a,b \in \mathbb{Z})\) is equal to |a –b| or |b – a|. Find the distance between points a and b on the number line when:

a. a = -3; b = 5

b. a = 15; b = 37

**Question 3: **Find the integers a and b that satisfy:

a. |a| + |b| = 0

b. |a + 5| + |b – 2| = 0

### 3.2. Multiple choice exercises Bài

**Question 1: **If a + c = b + c then:

A. a = b

B. a < b

C. a > b

D. Both A, B, and C are wrong.

**Verse 2:** Let b ∈ Z and b – x = -9. Find x

A. -9 – b

B. -9 + b

C. b + 9

D. -b + 9

**Question 3: **Find x knowing x + 7 = 4

A. x = -3

B. x = 11

C. x = -11

D. x = 3

Show solution

**Question 4: **Which of the following integers x satisfy x – 8 = 20

A. x = 12

B. x = 28

C. x = 160

D. x = -28

**Question 5: **How many integers x are there such that x + 90 = 198

A. 0

B. 3

C. 2

D. 1

## 4. Conclusion

Through this lesson, you need to complete a number of goals that the lesson gives, such as:

- The property of equality
- Master the rules of transitions

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