EQUIVALENT EXPRESSIONS

Equivalent expressions are algebraic expressions that will work the same even if they look different. Two algebraic expressions are considered to be equivalent, if they have the same value, when we substitute in the same value(s) for the variable(s).

Examples 1 :

In (-5 + 3) and (3 - 5), the numbers  are presented in different orders, but both are equal to -2.

-5 + 3 = -2

3 - 5 = -2

So, (-5 + 3) and (3 - 5) are equivalent operations.

Examples 2 :

In 1/2 and 3/6, the numbers  are different, both are equal to 0.5.

1/2 = 0.5

3/6 = 0.5

So, 1/2 and 3/6 are equivalent fractions.

Examples 3 :

Consider the two expressions given below.

3(x + 2)

3x + 6

If you substitute the any and same real value for x in both the expressions, both of them will result the same value.

When x = -1,

3(-1 + 2) = 3(1) = 3

3(-1) + 6 = -3 + 6 = 3

When x = 0,

3(0 + 2) = 3(2) = 6

3(0) + 6 = 0 + 6 = 6

When x = 2,

3(2 + 2) = 3(4) = 12

3(2) + 6 = 6 + 6 = 12

3(x + 2) = 3x + 6 for all real values of x

Therefore 3(x + 2) and 3x + 6 are equivalent algebraic expressions.

Generating Equivalent Algebraic Expressions

Write the equivalent algebraic expressions for the following :

Example 1 :

7(x - 3) + 2(2x - 5) - 3(x - 5)

Solution :

= 7(x - 3) + 2(2x - 5) - 3(x - 5)

Use Distributive Property.

= 7(x) + 7(-3) + 2(2x) + 2(-5) - 3(x) - 3(-5)

= 7x - 21 + 4x - 10 - 3x + 15

= 8x - 16

Example 2 :

4x - (2 + 4x) - 2(x - 1) - 8(x -3)

Solution :

= 4x - (2 + 4x) - 2(x - 1) - 8(x -3)

Use Distributive Property.

= 4x - 2 - 4x - 2(x) - 2(-1) - 8(x) - 8(-3)

= 4x - 2 - 4x - 2x + 2 - 8x + 24

= -10x + 24

Example 3 :

Solution :

Example 4 :

Solution :

Example 5 :

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Example 6 :

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Example 7 :

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Example 8 :

Solution :

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