Question

Fill in the blanks in the following proof :
Given :4x=8(x-2)
Prove : x=4

Answer 1

1.Given

2.4x=8x-16

3.Subtraction property

4.Division property

Explanation:

Answer 2

1. Given

2.
`4x=8x-16`

3. Subtraction property of equality.

4. Division property of equality.

Explanation:

You need to remember:

- Distributive property:

`a(b\±c)=ab\±ac`

- Subtraction property of equality:

If
`a=b`, then
`a-c=b-c`

- Division property of equality:

If
`a=b`, then
`(a)/(c)=(b)/(c)`

Then:

1. Given:

`4x=8(x-2)`

2. We must apply Distributive property:

`4x=8x-16`

3. Now we must apply the Subtraction property of equality. Subtracting
`8x` from both sides of the equation, we get:

`4x-(8x)=8x-16-(8x)\\\\-4x=-16`

4. Finally, we must apply the Division property of equality. Dividing both sides of the equation by -4, we get:

`(-4x)/(-4)=(-16)/(-4)\\\\x=4`