To perform a two column proof, we should give a statement and give a reason of it.
So we start with the initial statement.
1. Statement: x-4 =(1/2)(8x+6)+4x. Reason: Given
Next, we distribute the multiplication (1/2) with(8x+6). If we do so, we get the following statement.
2. Statement x-4 = (4x+3) + 4x. Reason: Distributive property of addition and multiplication.
Now, on the right we can add 4x with 4x, due to the associative property of additon, we get
3. Statement: x-4 = (4x+4x)+3 = 8x+3. Reason: Associative property of addition.
Now, we can subtract x on both sides, so we get
4. Statement: -4 = 7x+3. Reason: Subtraction property of equality.
By the same reason, we should subtract 3 on both sides. We get
5. Statement: -7 = 7x. Reason: Subtraction property of equality.
Finally, we divide by 7 on both sides, so we get
6. Statement: -1=x. Reason: Division property of equality.
7. Statement: x=-1. Reason: Symmetric property of equality.
