how do you solve a linear equation where there are unknowns on each side e.g. 4(k + 7) = 12k + 4

In order to solve this equation you want to get all of the unknowns on one side of the equal sign and all of the numbers on the other side. However, before you do this, the first step is to expand the bracket. To do this, you need to multiply everything in the bracket by 4. So 4 Multiplied by K is 4k and 4 multiplied by 7 is 28. So the equation is now written as 4k + 28 = 12 k + 4. Now we have done this, we can think about getting all of the Ks on the same side. If we look at the equation, 12K is bigger than 4K, so it makes sense to subtract 4 K from both sides. remember whatever you do to one side of the equation, you must do to the other. So 4K - 4K is 0 leaving us with 28 on the left handmade of the equation. 12K - 4K is 8K so the right hand side of the equation can now be written as 8K + 4. so the equation is 28 = 8K + 4. If you remember, we want to get all the numbers on one side and all the Ks on the other. We can do this by minusing 4 from each side. so we get 24 = 8k. The final step is to get K = a number. We can this by dividing both sides by 8 because that is the opposite to multiplying 8 by K. So 8K divided by 8 is K and 24 divided by 8 is 3. so we now have our answer k = 3. If we want to check this we can substitute K back into the equation to see if it works.