Question

Identify the reason for each step in the solution.

Answer 1

The properties or reasons for the given simplifications are:

1. Distributive property

2. Subtraction property of equality

3. Commutative property.

4. Subtraction property of equality.

5. Commutative property.

Explanation:

Given:

`3(x+2)=2x +3`

1.
`3x+6=2x+3`

Here, 3 is distributed among the terms in the parenthesis and multiplied to each of the terms inside the parenthesis.

So, the property used is distributive property of multiplication over addition.

2.
`3x+6-2x=2x+3-2x`

Here, 2x is subtracted from both sides. So, the equation remains the same due to the subtraction property of equality which says that subtracting same terms on both sides of the equality doesn't affect the equation.

3.
`x+6=3`

Now, simplifying
`3x - 2x` gives
`x`. Similarly, on the right side,
`2x - 2x` results in 0. This is the commutative property of combining like terms.

4.
`x+6-6=3-6`

Here, 6 is subtracted from both sides. So, the equation remains the same due to the subtraction property of equality which says that subtracting same terms on both sides of the equality doesn't affect the equation.

5.
`x=-3`

Again, we use commutative property and simplify for
`x`.

So, the properties or reasons for the above simplification are:

1. Distributive property

2. Subtraction property of equality

3. Commutative property.

4. Subtraction property of equality.

5. Commutative property.