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Generation of Equivalent Expression

Sep 17, 2022
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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.  

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

For example, let us consider the algebraic expression 

3x + 2x + 4 

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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. 

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 – 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) 
  1. 5(x+1) + 2(x–2) 
  1. 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 

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

=5x+5+2x−4  

=5x+2x+5−4 

=7x+1 

  1. 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

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