Solving Equations Using the Distributive Property

Introduction for distributive property:

An operation is distributive if the result of applying it to a sum of terms equals the sum of the results of applying it to the terms individually.
a ( b + c ) = ( a x b ) + ( a x c ).
Here, ‘a’ is multiplied with the sum of two terms ‘b and c’ in the left hand side which, gives the same answer when ‘a’ is multiplied individually with ‘b’ and ‘c’ and then added. Solving equations using the distributive property is very easy. Here we are going to see solving equations using the distributive property.

Distributive Property:

The types of distributive property used in solving equations are

a (b + c) = (a x b) + (a x c).

a (b - c) = (a x b) - (a x c).

These two are used for solving the equations.

Example Problems for Solving Equations Using the Distributive Property:

Example 1 for solving equations using the distributive property.

Solve the equation 10 (2 + 3) = (10 x 2) + (10 x 3).

Left hand side:

First take 10 (2 + 3)
By adding 2 + 3 we get 5
And now it is 10 (5)
So the answer for the Left hand side is 50

Right hand side:

Now we take (10 x 2) + (10 x 3)
By multiplying 10 with 2 and 10 with 3 we get (20) + (30)
And now we add 20 with 30
So the answer for Right hand side is 30
Hence proved Left hand side is equal to right hand side. Is this topic irrational number definition hard for you? Watch out for my coming posts.

Example 2 for solving equations using the distributive property.

Solve the equation 10(4 – 6) = (10 x 4) - (10 x 6).

Left hand side:

First take 10 (4 - 6)
By adding 4 - 6 we get -2
And now it is 10 (-2)
So the answer for the Left hand side is -20

Right hand side:

Now we take (10 x 4) - (10 x 6)
By multiplying 10 with 4 and 10 with 6 we get (40) - (60)
And now we subtract 40 with 60
So the answer for Right hand side is -20
Hence proved Left hand side is equal to right hand side.


Example 3 for solving equations using the distributive property.

Solve the equation 4(5 – 3) = (4 x 5) - (4 x 3).

Left hand side:

First take the 4(5 – 3)
By subtracting 5 – 3 we get 2
And now it is 4 (2)
So the answer for the Left hand side is 8

Right hand side:

Now we take (4 x 5) - (4 x 3)
By multiplying 4 with 5 and 4 with 3 we get (20) - (12)
And now we subtract 20 with 12
So, the answer for Right hand side is 8
Therefore, Left hand side is equal to right hand side.
Hence proved