Generation of Equivalent Expression

Key Concepts

• Use properties of operations to write equivalent expressions
• Write equivalent expressions by combining like terms
• Identify equivalent expressions

4.1 Generate equivalent expressions 

To generate an equivalent expression to another expression, we have to be aware of the parts of an algebraic expression.  

We can use properties to combine like terms in an expression. 

For example, let us consider the algebraic expression 

3x + 2x + 4 

You can add/subtract the coefficients of the like terms to combine them.  

3x + 2x + 4 = 5x + 4 

4.2.1 Use properties of operations to write equivalent expressions 

Equivalent expressions have the same value regardless of the value that is substituted for the same variable in the expression. 

Example 1: 

Use properties operation to write equivalent expressions. 

 – 1/2(x+8) 

Solution: 

-1/2(x+8) =-1/2x + (-1/2 ) . 8 

 =-1/2x +(-4) 

= -4 + (−1/2x)  

4.2.2 Write equivalent expressions by combining like terms  

Example1: 

Write an equivalent expression by combining the like terms. 

-6x+2y+4x 

Solution: 

-6x+5y+4x 

-6x + 4x+5y  

(-6+4) x+5y  

-2x+5y 

Example2: 

Write an equivalent expression by combining the like terms. 

2y+5y−5+8  

Solution: 

Combine the like terms of the first expression. 

Here, the terms 2y and 5y are like terms.  

So, add their coefficients. 2y+5y=7y. 

Also, −5 and 8 can be combined to get 3. 

4.2.3 Identify equivalent expressions 

Example1: 

Which of the expressions below is equaling? 

Solution: 

4(2x–1) = 4(2x) – 4(1)   

     = 8x – 4  

Example2: 

1. Which of the following expressions are equivalent to 7x+1?[Text Wrapping Break]2(2x−1) + 3(x+1) 

2. 5(x+1) + 2(x–2) 

3. 7(x–1) +2 

Solution:   

1. 2(2x−1) +3(x+1) =2(2x) +2(−1) +3(x)+3(1) 

=4x−2+3x+3  

=4x+3x−2+3 

=7x+1 

2. 5(x+1) +2(x−2) =5(x)+5(1) +2(x)+2(−2) 

=5x+5+2x−4  

=5x+2x+5−4 

=7x+1 

3. 7(x−1) +2 =7(x)+7(−1) +2 

=7x−7+2  

=7x−5 

Exercise:

1.    Write an equivalent expression. (a.) -3(8+5g) (b.) (x+6)+3y
2.    Use properties of operation to write an expression equivalent to 5x +  +3x-3.
3. Use the associative property to write an expression equivalent to (w + 6) +4.
4.    Which of the following expressions is equivalent to 4x-3 for all values of x?
5. 2(2x−3)
6. 2(2x-1)-1
7. 2(2x+1)-4
8. Write an equivalent expression to 5(x-1) +7.                    
9.  Which expressions are equivalent to -6n +(-12) +4n?
10. 4(n-3)-6n
11. 2(2n-6)
12. Andre wrote the expression —2 + 4x ÷3 to represent the relationship shown in the table.

Write two other expressions that also represent the relationship shown in the table.

8. Write equivalent expressions by combining the like terms.

            4x + 3x + 5y

9. Write equivalent expressions by combining the like terms.

           3x + 2y + 4x + 7 – y.                       

10. Use properties of operation to write an expression equivalent to 6x +  + 4x – 4.

Concept Map

What have we learned:

• Understand equivalent expressions
• Understand how to use properties of operations to write equivalent expressions
• Identify like terms
• Write equivalent expressions by combining like terms
• Identify equivalent expressions