# What is the algebra equation and how to translate words into algebra equation?

- Using an equal sign to express the equal relation of two algebra expressions is called the equation.

- Example 1:
- The words expression is : If the width of a rectangle is twice the length of the rectangle, find its area.

- Solution:
- Let x be the length of the rectangle, then its width is 2x,
- The equation is : The area of the rectangle = x ( 2x ), that is, Area of the rectangle = 2x
^{2}
- Note: The area of a rectangle is the product of its length and width.

- Example 2:
- The words expression is: The sum of three consecutive integers is 24, what are the three integers?

- Solution:
- Let x, x + 1, and x + 2 be the three consecutive integers. Since the sum of the three consecutive integers is 24
- The equation is : x + x + 1 + x + 2 = 24 -> 3x + 3 = 24 -> 3x = 24 - 3 -> 3x = 21 -> x = 7
- The three integers are 7, 8 , 9.
- Note: the word 'is' represent an equal relation.

- Example 3:
- The words expression is: Alice is eleven years order than her brother John. Three years ago, the sum of their ages was 21 years.
How old are Alice and John now?

- Solution:
- Let A be Alice and J be John. Since Alice is 11 years older than her brother John, then the equation is A = J + 11
- Three years ago, the age of Alice was A - 3, the age of John was J - 3. Since three years ago, the sum of their ages was 21 years, the age equation was:
- A - 3 + J - 3 = 21 -> A + J - 6 = 21 -> A + J = 21 + 6 -> A + J = 27
- Substitute equation A = J + 11 into the equation A + J = 27
- J + 11 + J = 27 -> J + J = 27 - 11 -> 2J = 16 -> J = 8, A = J + 11 = 8 + 11 = 19
- Therefore, Alice is 19 years old and John is 8 years old now.