Question

How do you solve the equation for `z`: `4(2z - 3) = 7(z + 5)`?

Answer 1

There are several steps.

Explanation:

I will remove parentheses, then collect all terms involving the unknown on one side and all terms not involving the unknown on the other side. I then expect to divide by the coefficient of the unknown.

`4(2z - 3) = 7(z + 5)`

Remove parentheses by using the distributive property (of multiplication over addition and subtraction).

`4(2z) - 4(3) = 7(z) +7(5)`

`8z-12 = 7z +35`

Subtract `7z` and add `12` on both sides:

`8z - 7z = 35 +12`

`z = 47`

In this case, the coefficient of the unknown (the number in front of `z`) is `1` (not written), so I do not need to divide. We can see that the solution is:

`47`

The solution set is: `{47}`.