Equivalent equations are equations that have the same solution sets. They are represented by the symbol "⇔". The document provides an example of equivalent equations 3x + 6 = 9 and x + 2 = 3, which have the same solution x = 3. It also discusses methods for solving equations with fractions, such as changing the equation into an equivalent equation without fractions by multiplying both sides by the lowest common multiple. Word problems can be solved by understanding the information given, representing the unknown as a variable, writing a mathematical model based on the information, solving the model, and checking the solution.

1. Equivalent Equations
Equivalent equations are equation which have the same solution
sets if a certain operation is applied to the equations. Equivalent
equations are symbolized by the symbol ”⇔”
Equation 3x + 6 = 9 and x + 2 = 3
have the same solution. So, they
are equivalent.
Do equations 3x + 6 = 9 and x + 2
= 3 have the same solution?

2. Exercise
Try to make some examples of
“Equivalent Equations”!

3. Solving Equation of Fraction Form
Solution:
Method I :
⇔
⇔
⇔
⇔
⇔
⇔
⇔
⇔
Both sides are multiplied by 5Both sides are multiplied by 5
Both sides are added by 4Both sides are added by 4
Both sides are divided by 6Both sides are divided by 6
Determine the solution of equation ( ) 623
5
2
=−x
( ) 623
5
2
=−x

4. Method II :
⇔
⇔
⇔
⇔
⇔
⇔
6
5
4
5
6
=−x
5
4
6
5
4
5
4
5
6
+=+−x
5
4
6
5
6
=x
5
34
6
5
5
6
6
5
×=× x
6
34
=x
6
4
5=x
Both sides are added byBoth sides are added by
5
4
Both sides are multiplied byBoth sides are multiplied by
6
5
( ) 623
5
2
=−x

5. To determine the solution of fraction equation is by using some
methods:
1. Change the equation into an equivalent equation but doesn’t consist
of fraction anymore. By multiplying with its LCM
2. Without changing the equation into a kind of equivalent equation
An equation in fraction form, is an equation that its variable
consist of fraction or the Constanta is in fraction form, or both
of them are in fraction form.

6. Application of Linear Equation with
One Variable in Daily Life
One variable equation is often used in the daily life. If you face a word
problem, pay attention to the following several things.
1.Comprehend the problem so you acquire the known things and the
question.
2.State the questions in variables, such as x.
3.Write the mathematical model / sentence according to the known
situation.
4.Solve the mathematical sentence.
5.Recheck the solution.

7. The Following are Several Terms commonly
Used in a Word Problem and How to Write it
No Terms How to Write
1. The sum of m and n m + n
2. The difference between m and n m-n
3. Product of m and n m × n
4. Quotient m : n
5. The inverse of m
6. Inverse of the sum of m and n
7. Inverse of the difference between m
and n, m > n
8. Square of sum of m and n (m+n)2
9. Sum of square of m and n m2
+ n2
10. Square of difference m and n (m-n)2
11. Difference of square of m and n, m2
> n2
m2
- n2